I have an integral whose upper and lower limits depends on the probabilty distribution chosen for the variable, $x$, I am integrating on. For example, if I consider that $x$ is normally distributed the integral is defined on $[-\infty,+\infty]$, while if $x\sim U[-a,a]$ the integral is defined on $[-a,+a]$.
Given that I don't want to specify a distribution, I was wondering how to write down the integral and let the reader understand that the integral is defined on the support of the variable $x$.
Thanks, Giancarlo