I would like to know the value of the following improper integral: $$\int \limits_{-\infty}^{\infty}\frac{2x}{1+x^2}dx$$
as the function $f(x)=\displaystyle\frac{2x}{1+x^2}$ satisfies $f(-x)=-f(x)$ can I immediately conclude that the integral is equal to zero?
Thank you in advance for any suggestion.