For $F=yx^3\hat{i}+y^2\hat{j}$ compute the line integral $\int\_C F\cdot dr$ where $C$ is the curve $y = x^2$ for $0\le x\le 1$.

Can this be solved with Green's Theorem? I am aware of the method where everything is written in terms of x, but it seems like Green's theorem should work?