Best way to increment Integer in arrayList in Java

You can't increment the value in place since Integer objects are immutable. You'll have to get the previous value at a specific position in the ArrayList, increment the value, and use it to replace the old value in that same position.

int index = 42; // whatever index
Integer value = ints.get(index); // get value
value = value + 1; // increment value
ints.set(index, value); // replace value

Alternatively, use a mutable integer type, like AtomicInteger (or write your own).

Maybe you need to use another structure of data?

LinkedList<AtomicInteger> ints = new LinkedList<AtomicInteger>();
ints.add(new AtomicInteger(5));
ints.add(new AtomicInteger(9));

ints.getLast().incrementAndGet();