That's because the list is backed by the array, and arrays can't change their size.
But you could make a copy of the list returned by the asList method using
List ints = new ArrayList(
Arrays.asList(new Integer[] {new Integer(1), new Integer(2), new Integer(3)})
);
Then you'll have your six and ten.
By the way, wouldn't be "The Six and Ten" a nice name for a pub?
Bu.