What made i = i++ + 1; legal in C++17?
Before you start yelling undefined behaviour, this is explicitly listed in N4659 (C++17)
i = i++ + 1; // the value of i is incremented
Yet in N3337 (C++11)
i = i++ + 1; // the behavior is undefined
What changed?
From what I can gather, from [N4659 basic.exec]
Except where noted, evaluations of operands of individual operators and of subexpressions of individual expressions are unsequenced. [...] The value computations of the operands of an operator are sequenced before the value computation of the result of the operator. If a side effect on a memory location is unsequenced relative to either another side effect on the same memory location or a value computation using the value of any object in the same memory location, and they are not potentially concurrent, the behavior is undefined.
Where value is defined at [N4659 basic.type]
For trivially copyable types, the value representation is a set of bits in the object representation that determines a value, which is one discrete element of an implementation-defined set of values
From [N3337 basic.exec]
Except where noted, evaluations of operands of individual operators and of subexpressions of individual expressions are unsequenced. [...] The value computations of the operands of an operator are sequenced before the value computation of the result of the operator. If a side effect on a scalar object is unsequenced relative to either another side effect on the same scalar object or a value computation using the value of the same scalar object, the behavior is undefined.
Likewise, value is defined at [N3337 basic.type]
For trivially copyable types, the value representation is a set of bits in the object representation that determines a value, which is one discrete element of an implementation-defined set of values.
They are identical except mention of concurrency which doesn't matter, and with the usage of memory location instead of scalar object, where
Arithmetic types, enumeration types, pointer types, pointer to member types,
std::nullptr_t, and cv-qualified versions of these types are collectively called scalar types.
Which doesn't affect the example.
From [N4659 expr.ass]
The assignment operator (=) and the compound assignment operators all group right-to-left. All require a modifiable lvalue as their left operand and return an lvalue referring to the left operand. The result in all cases is a bit-field if the left operand is a bit-field. In all cases, the assignment is sequenced after the value computation of the right and left operands, and before the value computation of the assignment expression. The right operand is sequenced before the left operand.
From [N3337 expr.ass]
The assignment operator (=) and the compound assignment operators all group right-to-left. All require a modifiable lvalue as their left operand and return an lvalue referring to the left operand. The result in all cases is a bit-field if the left operand is a bit-field. In all cases, the assignment is sequenced after the value computation of the right and left operands, and before the value computation of the assignment expression.
The only difference being the last sentence being absent in N3337.
The last sentence however, shouldn't have any importance as the left operand i is neither "another side effect" nor "using the value of the same scalar object" as the id-expression is a lvalue.
Answer
In C++11 the act of "assignment", i.e. the side-effect of modifying the LHS, is sequenced after the value computation of the right operand. Note that this is a relatively "weak" guarantee: it produces sequencing only with relation to value computation of the RHS. It says nothing about the side-effects that might be present in the RHS, since occurrence of side-effects is not part of value computation. The requirements of C++11 establish no relative sequencing between the act of assignment and any side-effects of the RHS. This is what creates the potential for UB.
The only hope in this case is any additional guarantees made by specific operators used in RHS. If the RHS used a prefix ++, sequencing properties specific to the prefix form of ++ would have saved the day in this example. But postfix ++ is a different story: it does not make such guarantees. In C++11 the side-effects of = and postfix ++ end up unsequenced with relation to each other in this example. And that is UB.
In C++17 an extra sentence is added to the specification of assignment operator:
The right operand is sequenced before the left operand.
In combination with the above it makes for a very strong guarantee. It sequences everything that happens in the RHS (including any side-effects) before everything that happens in the LHS. Since the actual assignment is sequenced after LHS (and RHS), that extra sequencing completely isolates the act of assignment from any side-effects present in RHS. This stronger sequencing is what eliminates the above UB.
(Updated to take into account @John Bollinger's comments.)