$\int_{- 1}^{1} [{cos}^{- 1} x] d x$ (where $[\cdot]$ denotes greatest integer function).

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Solution

$\int_{- 1}^{1} [{cos}^{- 1} x] d x$
= $\int_{- 1}^{C o s 3} [{cos}^{- 1} x] d x$ + $\int_{C o s 3}^{C o s 2} [{cos}^{- 1} x] d x$ + $\int_{C o s 2}^{C o s 1} [{cos}^{- 1} x] d x$ + $\int_{C o s 1}^{1} [{cos}^{- 1} x] d x$
= Cos1+Cos2 +Cos3+3

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