How to prove that this integral converges absolutely?

Question

$f:[a,{\infty}[\to\mathbb{R}\ $ is bounded and suppose that $f$ is integrable on each interval of the form $[a,b[$. Prove that $$\int_0^\infty \frac { f(x) }{ x^p } \ \, dx$$ converges absolutely for $p>1$. Conclude that, if $x^pf(x)$is bounded for some $p>1$, then $$\int_a^\infty f\ \, dx$$ converges absolutely.