Are Java wrapper classes really immutable?

The compiler autoboxes primitive values, this means that

Integer value = 6;

will be compiled as

Integer value = Integer.valueOf(6);

Integer.valueOf will return an Integer instance with the given value. In your case i will now reference the Integer(6) instead of the Integer(5), the Integer(5) object itself will not change.

To see this you can do following

Integer i = new Integer(5);//assign new integer to i
Integer b = i;//b refences same integer as i
i = 6;//modify i
System.out.println(i +"!="+b);

This will print 6!=5, if the integer instance had been modified it would print 6!=6 instead.

To clarify this is only meant to show how an assignment to Integer only modifies the reference and does not alter the Integer instance itself. As user @KNU points out it does not prove or show the immutability of Integer, as far as I can tell the immutability is only indirectly given by the lack of modifying methods in its API and the requirement that instances returned by Integer.valueOf have to be cached for a certain range.

i is a reference. Your code change the reference i to point to a different, equally immutable, Integer.

final Integer i = Integer.valueOf(5);

might be more useful.

Immutable means that the object state cannot be changed. In your case you haven't changed the object new Integer(5), but you have changed the reference i to point to another object. Hope it is clear:)