Vector Calculus · Superchallenge problem

Let $C$ be the boundary of the lens-shaped region common to the disks $x^2 + y^2 \le 1$ and $(x - 1)^2 + y^2 \le 1$, traversed once counterclockwise. Evaluate $\displaystyle\oint_C \left(e^x - y^3\right)dx + \left(x^3 + \cos y\right)dy$. Give an exact answer.