Find

$\frac{d}{dx}[{\displaystyle \underset{3x}{\overset{x^2}{}}}\frac{t-1}{t^2+1}dt]$

$($a$)\frac{d}{dx}[{\displaystyle \underset{x}{\overset{a}{}}}f(t)dt]=-f(x)$

by writing

${\displaystyle \underset{3x}{\overset{x^2}{}}}\frac{t-1}{t^2+1}dt={\displaystyle \underset{3x}{\overset{0}{}}}\frac{t-1}{t^2+1}dt+{\displaystyle \underset{0}{\overset{x^2}{}}}\frac{t-1}{t^2+1}dt$