As we all know:
$\int_{a}^{\infty} \frac{1}{x^p}$ converges iff $p>1$ ($a>0$)
$\int_{0}^{a} \frac{1}{x^p}$ converges iff $p<1$ ($p, a >0 $).
Is there exists any similar claims for $\int_{-\infty}^{a}$ in 1, and $\int_{-a}^{0}$ in 2?
In dirichlet theorem and the integral test of converging, in all sources (as I guess) they state the claim foe functions $f,g$ defined on $[a,\infty)$. Does it also hold if $f,g$ are defined on $(-\infty,a]$?