Read through the last part of §5.5 very carefully.
Pay careful attention to the last two Examples.

Sometimes we can take advantage of little "tricks" to make integration problems a little easier to manage. Symmetry helps with this.

If you want to integrate $\displaystyle {\int_{{-{6}}}^{{10}}}\frac{{{5}{t}^{{3}}-{8}{t}}}{{{t}^{{2}}+{1}}}{\left.{d}{t}\right.}$, we can make the problem a little easier by noting that $\displaystyle {\int_{{-{6}}}^{{10}}}\frac{{{5}{t}^{{3}}-{8}{t}}}{{{t}^{{2}}+{1}}}{\left.{d}{t}\right.}={\int_{{a}}^{{10}}}\frac{{{5}{t}^{{3}}-{8}{t}}}{{{t}^{{2}}+{1}}}{\left.{d}{t}\right.}$, where $\displaystyle {a}>{0}$.

What is the value of $\displaystyle {a}$?
$\displaystyle {a}=$
Hint: What type of function is the integrand?