Stokes Theorem Help Needed!

Use Stokes' Theorem to evaluate

$\displaystyle \int F \cdot dr C\ is\ oriented\ counterclockwise\ as\ viewed\ from\ above. $

$\displaystyle F(x,y,z) = x i + y j + (x^2 + y^2) k $

$\displaystyle C\ is\ the\ boundary\ of\ the\ part\ of\ the\ paraboloid\ z = 1 - x^2 - y^2 in\ the\ first\ octant\ $

C is the boundary of the part of the paraboloid $\displaystyle z = 1-x^2-y^2 $ in the first octant.

The formula for stoke's theorem is $\displaystyle \int F \cdot dr = \int\int curl \cdot dS $

I went ahead and found the curl which is (2y-2x)k. So, when i set up the double integral, so far i have $\displaystyle \int\int (2y-2x)dA $

However, im having trouble with figuring out the bounds. I think this is a sphere, so does that mean i have to use spherical coordinates? Is there a simpler way because im really not good with spherical coordinates! Thanks.