Evaluate $\int_{-1}^{1} \left(x^{5} + 3 x\right)\,dx$.

Explanation

1. 01

   $f(-x) = -f(x)$ for $f(x) = x^{5} + 3 x$: the function is odd.

2. 02

   The integral of an odd function over $[-a, a]$ is 0: the area below the axis cancels the area above it.