It is difficult to explain how to do this without a 3-d plot.
But you end up if you closed solid. You then divide this solid into to parts. One composed of and the upper surface of, . Then, you prodced to find,
, where is solid formed. Understand? I realize it is difficult to be clear on this example.
Below is the curve of the region.
Divide it into 2 parts (the green and red)
Thus, the volume is (respectively),
Recognize that these are type II regions of integration,