JEE Math Practice Question

Let $$f(x)$$ be a function satisfying $$f(x)+f(\pi-x)=\pi^{2}, \forall x \in \mathbb{R}$$. Then $$\int\limits_{0}^{\pi} f(x) \sin x d x$$ is equal to :

1. A.$$\pi^{2}$$
2. B.$$\frac{\pi^{2}}{2}$$
3. C.$$2 \pi^{2}$$
4. D.$$\frac{\pi^{2}}{4}$$