Find the areas of uniform convergence, continuity, differentiability of the integral
$$I(\alpha )=\int_{0 }^{+\infty}\frac{\cos(\alpha x)}{1+x^{2}}dx$$
I do not know how to apply the Cauchy or Weierstrass criterion here. Are they actually needed in this case? And also having no ideas how to investigate the continuity and differentiability