Let \(f\left(x\right)=x+\frac{a}{{\pi }^{2}-4}\sin x+\frac{b}{{\pi }^{2}-4}\cos x\), \(x\in R\) be a function which sati…

Let \(f\left(x\right)=x+\frac{a}{{\pi }^{2}-4}\sin x+\frac{b}{{\pi }^{2}-4}\cos x\), \(x\in R\) 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)]