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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