Evaluate: $\int\limits_{-1}^{1} |x^4 - x| dx$

1

The correct answer is Option (2) → 1

$\int\limits_{-1}^{1} |x^4 - x| dx=\int\limits_{-1}^{1} |x(x-1)(x^2 + x + 1)|dx$

$∴I = \int\limits_{-1}^{0} (x^4 - x) dx + \int\limits_{0}^{1} -(x^4 - x) dx$

$I = \left[ \frac{x^5}{5} - \frac{x^2}{2} \right]_{-1}^{0} - \left[ \frac{x^5}{5} -\frac{x^2}{2} \right]_{0}^{1}$

$I= \left(\frac{1}{5} + \frac{1}{2} \right)- \left( \frac{1}{5} - \frac{1}{2} \right)$

$I = \frac{1}{2} + \frac{1}{2} = 1$