$\huge \int_{-\frac{\pi}{2}}^{ \frac{\pi}{2} } \sin\pa{x}^4 \cos x \d x $ $\huge \begin{align} \let u &= \sin x\\ \let \d u &= \cos ( x) \d x \\ \int_{-\frac{\pi}{2}}^{ \frac{\pi}{2} } \sin\pa{x}^4 \cos x \d x &= \int_{-1}^{1} u^4 \d u\\ &= 0.2\cdot 1^5 - 0.2\cdot 1^{-5} \\ &= 0.4 \end{align} $