Let $$f(x) = x + \frac{a}{\pi^2-4}\sin x + \frac{b}{\pi^2-4}\cos x$$, $$x \in \mathbb{R}$$ be a function which satisfies $$f(x) = x + \int_0^{\pi/2} \sin(x+y)f(y)dy$$. Then $$(a+b)$$ is equal to

A

$$-\pi(\pi+2)$$

B

$$-2\pi(\pi+2)$$

C

$$-2\pi(\pi-2)$$

D

$$-\pi(\pi-2)$$