I have a curve which starts on $(-2,0)$ then goes to $(2,0)$ along the curve $y=4-x^2$ then back to the point $(-2,0)$ along the curve $y=x^2-4$. I have to compute the line integral
$$\int -4x^2y \ dx -(x^3+y^3) \ dy$$
using Green's theorem. I know how to do Green's theorem with the partial derivatives but I don't quite understand how it being along the two curves makes a difference. Would I apply Green's theorem twice? Thank you.