the simplest example is if you have
\int \frac{f(x)}{\text{i$\epsilon $}+x} \, dx
so sometimes it is usefull to rewrite it in way
\int \frac{f(x)}{\text{i$\epsilon $}+x} \, dx=P \int \frac{f(x)}{x} \, dx-i \pi f(x)
where P means that you integrate in terms of principal value