This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
You can't, really. You can set the element to null or 0, or you can move all the other elements down by one and set the last element to null or zero. In either case, the array will still be the same size.
What you can do is allocate a new array one element shorter, and copy all the elements you want to keep into the new array.
If you don't like the way this sounds -- and you shouldn't! -- consider using a List<Integer> instead of an int.