# How to numerically solve an integral equation with a Cauchy principle kernel?

Consider such a Fredholm equation of $f(x)$:

$$f(x) = g(x) + \lim_{\epsilon \rightarrow 0^+ }\int_{-\infty}^{+\infty} \frac{d y V(x-y)}{a^2+ i \epsilon - y^2} f(y) .$$

Here $V(y)$ is a nice function of $y$ with $\lim_{|y|\rightarrow \infty } V(y) = 0,$ so is $g(x)$ too. The parameter $a >0$.

Apparently, the kernel has some singularity. So how to solve it numerically?