This doesn’t have anything to do with immutability of integers; it has to do with the fact that Java is Pass-by-Value, Dammit! (Not annoyed, just the title of the article :p )
To sum up: You can’t really make a swap method in Java. You just have to do the swap yourself, wherever you need it; which is just three lines of code anyways, so shouldn’t be that much of a problem 🙂
Thing tmp = a;
a = b;
b = tmp;