The convolution of two distribution functions $F_1$ and $F_2$ is
$F(t) = \int_{0}^{t} F_2(t-x) dF_1(x)$.
This can also be expressed as
$F(t) = \int_{0}^{t} F_1(t-x) dF_2(x)$.
The similar expression holds for survival function also. Now, I am reading a book which mentions that
$\bar F(t-u) = \int_{-\infty}^{\infty} \bar F_1(t-s) f_2(s-u) ds$,
where $f_2$ is the density of $F_2$. I am unable to understand how are we getting the above step, esp. how is the upper limit changing to $\infty$. Can anybody please explain it?