Problems with integration word problems

I was absent the day that we covered these, and have yet to have received a sufficient explanation of how to do them. I understand integration fairly well, but I'm unsure of how to exactly apply it in these problems. One excellent example is this:

The Washington Monument is around 550 ft. tall. If you're trying to throw an object from gound level to the top of the Monument, what would your initial velocity need to be? Gravity is at -32 ft/s, don't worry about air resistance.

I understand how to integrate, but I don't know how to begin to apply it to this kind of a problem. Thanks in advance for all the advice.