JEE Math Practice Question

Let $$f(x) = x + {a \over {{\pi ^2} - 4}}\sin x + {b \over {{\pi ^2} - 4}}\cos x,x \in R$$ be a function which satisfies $$f(x) = x + \int\limits_0^{\pi /2} {\sin (x + y)f(y)dy} $$. then $$(a+b)$$ is equal to

1. A.$$ - 2\pi (\pi + 2)$$
2. B.$$ - \pi (\pi - 2)$$
3. C.$$ - \pi (\pi + 2)$$
4. D.$$ - 2\pi (\pi - 2)$$