The value of $\int_{-1}^1 x^2 e^{\left[x^3\right]} d x$, (where $[t]$ denotes the greatest integer $\leq t$ ), is: [JEE Main 2021, 25 Feb (Shift 1)]

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The value of \(\int_{-1}^1 x^2 e^{\left[x^3\right]} d x\), (where \([t]\) denotes the greatest integer \(\leq t\) ), is:…