Vector Calculus · Challenge problem

Let $C$ be the upper half of the circle $x^2 + y^2 = 2x$, traversed from $(2, 0)$ to $(0, 0)$. Evaluate $\displaystyle\int_C \left(e^x\sin y + 3y\right)dx + \left(e^x\cos y + x^2\right)dy$. Give your answer in terms of $\pi$.