# What is the integral of int dx/(1+x^2)  from -1 to 1?

$\frac{\pi}{2}$
$\int \frac{\mathrm{dx}}{1 + {x}^{2}} , \left[- 1 , 1\right] = {\tan}^{-} 1 \left(x\right) , \left[- 1 , 1\right]$
$= {\tan}^{-} 1 \left(1\right) - {\tan}^{-} 1 \left(- 1\right)$
$= \frac{\pi}{2}$