# Functions and Integrals 1

Calculus Level 4

Let $$f: \mathbb R \to \mathbb R$$ be defined as $$f(x) = \sin x + x$$. If $$\displaystyle \int_0^\pi f^{-1} (x) \, dx = \dfrac{\pi^2}2 - k$$, find the value of $$k$$.

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