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

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!