Vector Calculus · Superchallenge problem

For $a > 0$ let $C_a$ be the curve $y = a\sin x$ from $(0,0)$ to $(\pi, 0)$. Find the minimum, over all $a > 0$, of the work $\displaystyle\int_{C_a}(1 + y^3)\,dx + (2x + y)\,dy$. Give your answer in terms of $\pi$.