Find integral from 1 to infinity of $1/(1+x^2)$ I am practicing for an exam and am having trouble with this problem. Find the integral from 1 to infinity of $\frac{1}{1+x^2}$. I believe the integral's anti-derivative is $\arctan(x)$ which would make this answer $\arctan(\infty)-\arctan(1)$ but from here I'm lost. I did find out that this comes out to $\pi/4$ but I don't know why.

The key point is that you do not evaluate the antiderivative at $\infty$ since most functions aren't defined for $x=\infty$. You take the limit: $$\int_a^{\infty}f(x)dx=\lim_{m \to \infty}\int_a^{m}f(x)dx=\lim_{m \to \infty}F(m)-F(a).$$
(It's punny because I'm Limitless.)
