# Doubt on the equation 8.11.9 ( Green's function's construction ). How do they take limit of the integral?

Reference:

Linear Partial Differential Equations for Scientists and Engineers(Authors:-Tyn Myint-U, Lokenath Debnath)

I understood till the red box. I have doubt on the equation in the red box. How do they take limits of the integral? I don't understand. Please help me. What is the motivation behind the Green's function? Already there is a 'Variation Parameter' Technique is there no for finding the particular integral. Please explain.