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 \…

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 \( f(x)=x+\int_{0}^{\pi / 2} \sin (x+y) f(y) d y \). Then \( (a+b) \) is equal to

[JEE Main 2023, 29 Jan (Shift 1)]