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$\int_{- 2}^{2} \frac{\sin^{- 1} (\sin x) + \cos^{- 1} (\cos x)}{(1 + x^{2}) (1 + [\frac{x^{2}}{5}])} d x = (w h e r e [.] r e p r e s e n t s t h e g r e a t e s t i n t e g e r f u n c t i o n)$

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Correct option is C

I=∫−22 sin−1(sinx)+cos−1(cosx)1+x21+x25dxsin−1(sinx) is an odd function Also −2

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∫−22sin−1sinx+cos−1cosx1+x21+x25 dx=(where [. ] represents the greatest integer function)

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$\int_{- 2}^{2} \frac{\sin^{- 1} (\sin x) + \cos^{- 1} (\cos x)}{(1 + x^{2}) (1 + [\frac{x^{2}}{5}])} d x = (w h e r e [.] r e p r e s e n t s t h e g r e a t e s t i n t e g e r f u n c t i o n)$