Definite Integration

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