I want to save some integers after application shut down and restore them after application opening, what is the easiest way to do this?
You should store and load data from NSUserDefaults:
NSUserDefaults *defaults = [NSUserDefaults standardUserDefaults];
// to store
[defaults setObject:[NSNumber numberWithInt:12345] forKey:@"myKey"];
[defaults synchronize];
// to load
NSNumber *aNumber = [defaults objectForKey:@"myKey"];
NSInteger anInt = [aNumber intValue];