Inversion Game Real Strong

Calculus Level 5

A function $f$ is defined as $f(x) = \sin x + 2x$ .

Evaluate $\large \displaystyle \int _{2+\sin \left(1\right)}^{4+\sin \left(2\right)}f^{-1}(x) \ dx$ correct to 3 decimal places.

Clarifications: $f^{-1}(x)$ denotes the inverse of $f(x)$ , i.e. if $y = f(x)$ , then $x = f^{-1}(y)$ .