Explanation

(d)
Let $I = \int_{0}^{1}\frac{x^{4} + 1}{x^{2} + 1}\ dx$
$= \int_{0}^{1}\frac{x^{4} + 1 - 1 + 1}{x^{2} + 1}\ dx$
$= \int_{0}^{1}\left\lbrack \frac{x^{4} - 1}{x^{2} + 1} + \frac{2}{x^{2} + 1} \right\rbrack\ dx$
$= \int_{0}^{1}{\left( x^{2} - 1 + \frac{2}{x^{2} + 1} \right)dx}$
$= \left\lbrack \frac{x^{3}}{3} - x + 2\tan^{- 1}x \right\rbrack_{0}^{1}$
$= \left\lbrack \frac{1}{3} - 1 + 2\tan^{- 1}(1) - 0 \right\rbrack$
$= - \frac{2}{3} + 2.\frac{\pi}{4} = \frac{3\pi - 4}{6}$