Explanation

(c)
Let $I = \int_{- 1}^{1}{\frac{17x^{5} + 29x^{3} - 31\ x}{x^{2} + 1}dx - \int_{- 1}^{1}{\frac{x^{4} - 1}{x^{2} + 1}dx}}$
$= 0 - 2\int_{0}^{1}{\frac{\left( x^{2} - 1 \right)(x^{2} + 1)}{(x^{2} + 1)}dx}$
$= - 2\left\lbrack \left( \frac{x^{3}}{3} - x \right) \right\rbrack_{0}^{1} = \frac{4}{3}$