Are you looking for suggestions on how to solve integral equations or how integral equations are used in real world applications? The attached paper describes both plus I have more information if you're interested.
It depends on which kind of integral equation you have. If it is a Fredholm second kind linear equation you can consult the monograph of K.E. Atkinson
"The numerical solution of integral equations of the second kind". For other type of integral equation you can consult the book of Kress. For singular integral equations there is the Prossdorf-Silbermann book and so on.