Explanation on expectation of Cauchy mean

Question

It might seem trivial but I couldn't understand where the number 2 (highlighted) came from in the last equality of the following text. Could you please explain? Thanks.

Answer 1

\begin{align} \int_{-\infty}^{\infty}\frac{|x|}{\pi}\frac{1}{1+x^2}dx &= \int_{0}^{\infty}\frac{|x|}{\pi}\frac{1}{1+x^2}dx + \int_{-\infty}^{0}\frac{|x|}{\pi}\frac{1}{1+x^2}dx \\ &= \int_{0}^{\infty}\frac{x}{\pi}\frac{1}{1+x^2}dx - \int_{-\infty}^{0}\frac{x}{\pi}\frac{1}{1+x^2}dx \\ \end{align} Taking $t = -x$ in the $2^{nd}$ integral, it evaluates to - \begin{align} \int_{-\infty}^{0}\frac{x}{\pi}\frac{1}{1+x^2}dx &= \int_{\infty}^{0}\frac{-t}{\pi}\frac{1}{1+(-t)^2}d(-t) \\ &= - \int_{0}^{\infty}\frac{t}{\pi}\frac{1}{1+t^2}dt \\ \end{align} Thus, \begin{align} \int_{-\infty}^{\infty}\frac{|x|}{\pi}\frac{1}{1+x^2}dx &= 2\int_{0}^{\infty}\frac{x}{\pi}\frac{1}{1+x^2}dx \\ \end{align}