[Math] Conditional or absolute convergence of an integral $\int_{0}^{\infty}\frac{\sin x}{1+x^{2}}dx$

Question

I ran into a few problems where i had to check absolute\conditional convergence of a few integrals.

I'm sure theres a method to check this, i just can't find the trick.

I wan't help with one of the problems so that i can get the rest on my own.

Check absolute or conditional convergence of the integral:

$$\int_{0}^{\infty}\frac{\sin x}{1+x^{2}}dx$$

thanks in advance,

yaron

Answer 1

Compare with $$\int_0^\infty {dx\over 1 + x^2}$$.