The value of the integral, $\int\limits_1^3 {[{x^2} - 2x - 2]dx} $, where [x] denotes the greatest integer less than or equal to x, is :

Question

$-$ 5

$ - \sqrt 2 - \sqrt 3 + 1$

$-$ 4

$ - \sqrt 2 - \sqrt 3 - 1$

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