What exactly does comparing Integers with == do?

EDIT: OK, OK, I misread. I'm not comparing an int to an Integer. Duly noted.

My SCJP book says:

When == is used to compare a primitive to a wrapper, the wrapper will be unwrapped and the comparison will be primitive to primitive.

So you'd think this code would print true:

    Integer i1 = 1; //if this were int it'd be correct and behave as the book says.
    Integer i2 = new Integer(1);
    System.out.println(i1 == i2);

but it prints false.

Also, according to my book, this should print true:

Integer i1 = 1000; //it does print `true` with i1 = 1000, but not i1 = 1, and one of the answers explained why.
Integer i2 = 1000;
System.out.println(i1 != i2);

Nope. It's false.

What gives?