How does integration of a signal change the spectrum?
It is the basic property of Fourier Transforms. Given that $g(t)$ and $G(f)$ are Fourier transform pairs i.e.
$g(t)  \rightleftharpoons G(f)$
then
$\int_{-\infty}^tg(\tau)d\tau \rightleftharpoons \frac{1}{j2\pi f}G(f)$

This assumes that $G(0)=0$. If $G(0)$ is not zeros then the integral of $g(t)$ has a Fourier transform that includes a Dirac delta function.