Let \bold F(x,y,z)=(yx^2,-xz,3y). Consider the surface S of the paraboloid 2x=z^2+y^2 for 0\le x\le2. Compute the flux integral of curl of \bold F, (\nabla\times \bold F) through S.

I have an exam tomorrow and I want to know how to apply Stoke's Theorem here, how is the set up for the integral?

How can be done using line integral? I know a have to parametrize the surface, but I don't know how to set up the integral.

Please any help would be appreciated!