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

Let \(f(x)=x+\frac{a}{{\pi }^{2}-4}\sin x+\frac{b}{{\pi }^{2}-4}\cos x\), \(x\in R\) be a function which satisfies \(f(x)=x+{\int }_{0}^{\pi /2}\sin (x+y)f(y)dy\). Then \((a+b)\) is equal to

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