Inverse Area with definite integration.!

Calculus Level 4

If $f: \mathbb {R \to R}$ , $f(x)=x+\sin x$ , then find the value of

$\large \int_{0}^{\pi} f^{-1}(x) \ dx$

Note : $f^{-1}(x)$ denotes the inverse function of $f(x)$ .

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