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.