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Compute the integral from x to x^2 of (t^2 + sin t)

Compute the following integral

    \[ \int_x^{x^2} (t^2 + \sin t) \, dt. \]


The computation is as follows:

    \begin{align*}  \int_x^{x^2} (t^2 + \sin t) \, dt &= \left. \frac{t^3}{3} \right|_x^{x^2} - \cos t \biggr \rvert_x^{x^2} \\  &= \frac{x^6}{3} - \frac{x^3}{3} - \cos (x^2) + \cos x. \end{align*}

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