Well, I think the limits would be as follows:

z limit it bound by the plane and paraboloid.

For the cylindrical coordinates: You need to go the entire way around the circel(if you look at the paraboloid from top down in a 2D perspective it looks like a circle), so will go from to

Next, what is the radius?...by looking at the cylinder equation its 1.

Overall, this the limits should be:

Just remember to change to cylindrical coordinates after you have completed the first integral which is in cartesian.

Lastly, for checking your work, its pretty easy to use, I have an example written to get you started.

http://www.wolframalpha.com/input/?i...dx+from+0+to+1