The value of the integral, \( \int_{1}^{3}\left[x^{2}-2 x-2\right] ...

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The value of the integral, \( \int_{1}^{3}\left[x^{2}-2 x-2\right] d x \), where \( [\cdot] \)
P denotes the greatest integer less than or equal to \( x \) is:

W)
[JEE Main-2021 (February)]
(a) \( -5 \)
(b) \( -\sqrt{2}-\sqrt{3}+1 \)
(c) \( -4 \)
(d) \( -\sqrt{2}-\sqrt{3}-1 \)
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