Hey mrb165.

If the region you are integrating is not smooth (but continuous), then you will need to split up the integral into multiple parts. Since you have a paraboloid and a plane, there is a good chance of this happening.

To start you off in the right direction you should find where the x+y=1 plane intersections the paraboloid and look at partitioning the integral based on where this intersection is.

The analogy is that if you integrate say |x|dx over [-5,5] then you need to calculate [-5,0] and [0,5] when you are integrating.