Find $\int_{-1}^{1} \tan x d x.$

By Property 5, we can rewrite the integral given as

$$= \int_{-1}^{0}\tan x\,dx + \int_{0}^{1}\tan x\,dx$$

However, $\tan x$ is an odd function. That is, for every $x$ in its domain, $f(-x) = -f(x)$. Thus, the graph sections corresponding to the two terms above are symmetrical: