Obtain a parametrization of the curve c and use your result

Question

Parametrization for a line integral. Not sure if I'm parametrizing the curve correctly since it's in 3 space-- can I simplify it down to 2nd and parametrize the circle and parabola in the xy plane?

Let F(x,y,z))= 3yx²i + x³j + 3xyk be a vector field in R3 and C be the curve of intersection of the surface z = 2x+y² and the cylinder x² +y² = 4, oriented counterclockwise as viewed from above.

(a) Obtain a parametrization of the curve C and use your result to evaluate _surface∫_c F · dr.

(b) Use Stokes' theorem to evaluate _surface∫_c F · dr.