## Flux integral

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!