If $[t]$ denotes the greatest integer $\leq t$, then the value of $\int_{0}^{1}\left[2 x-\left|3 x^{2}-5 x+2\right|+1\right] \mathrm{d} x$ is :

Question

$\frac{\sqrt{37}+\sqrt{13}-4}{6}$

$\frac{\sqrt{37}-\sqrt{13}-4}{6}$

$\frac{-\sqrt{37}-\sqrt{13}+4}{6}$

$\frac{-\sqrt{37}+\sqrt{13}+4}{6}$

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