Explanation

(c)
$\int_{}^{}{e^{x}\left( \frac{1 - x}{1 + x^{2}} \right)^{2}dx} = \int_{}^{}{e^{x}\frac{(1 + x^{2} - 2x)}{\left( 1 + x^{2} \right)^{2}}dx}$
$= \int_{}^{}{e^{x}\left( \frac{1}{1 + x^{2}} - \frac{2x}{\left( 1 + x^{2} \right)^{2}}\ \right)dx}$
$= e^{x}.\frac{1}{1 + x^{2}} + \int_{}^{}\frac{2xe^{x}}{\left( 1 + x^{2} \right)^{2}}dx - \int_{}^{}\frac{2xe^{x}}{\left( 1 + x^{2} \right)^{2}}dx$
$= \frac{e^{x}}{1 + x^{2}} + c$