Nisha's response gave you a quick-and-dirty example of wrapping an int into an Integer object. I'll assume you follow how that's done so I won't dwell on wrapping ints into Integer objects, unless you ask for more on the topic.
You wrote that you will get integers from "the user." This makes me wonder precisely how the user will provide those numbers. If the user inputs the numbers while the program runs, then I assume you are aware that you are actually dealing with Strings and not int values, and that you'll have to convert each String to an Integer object. Shall I assume you have a handle on this part of the problem?
Another aspect of the problem that you need to deal with is the fact that Vectors store objects of the Object class. Consequenly you will have to do some casting of each Object to an Integer when you manipulate the vector objects. Are you aware of this, and are you able to do this part of the problem?
If you haven't been exposed to the Java API Specification web site, I strongly encourage you to visit it and start getting familiar with it. It is a bit overwhelming at first, but with some experience you will eventually get the hang of the organization and how to use the information. Visit http://java.sun.com/j2se/1.3/docs/api/index.html
At that address three windows appear, one in the upper left, one in the lower left, and one on the right.
Let's use class Vector as our first excuse to visit the site. When it first loads, all Classes are displayed by default, in the bottom left window. You use the top left window to select the Package you want to view. The bottom left window will display the classes in the Package you select in the top left window. Scroll through the list of classes (bottom left window) to find the one you're interested in and when you click on a class, it's specification will show in the large right window.
Being sure you have All Classes selected in the top left window, scroll throught the list in the bottom left window until you find Vector. Click it and you'll see the description of Class Vector appear in the large right window. A lot of information is presented...it'll overwhelm you if you've never done this before. But take the time to learn how it's organized. I'd suggest printing it...it'll take several pages, but I think it's worth the investment of paper and ink to help you get the feel of the kind of information and how it's presented.
First you'll see a general description of the class. You'll see that the Vector class comes from (inherited from) the java.lang.Object class. This is an important point because this is the basis for all Vector elements being of class Object. Scroll down a bit and you'll see a "Field Summary", a "Constructor Summary" and a "Method Summary". They all contain very useful information about the Vector class that you'll be using to solve your problem.
At this point, I'll terminate my response because I've gotten long-winded. What aspects of your problem do you need help on now?