Divergence of the amplitude for a Feynman diagram

[Raymont]

1. The problem statement
In calculating the amplitude for the diagram[1], view 1.jpg.
[1] Voja Radovanovic, Problem Book Quantum Field Theory

2. Homework Equations
View 2.jpg.

The Attempt at a Solution

View 3.jpg.[/B]
Why the integrals is divergent? Why the other terms are finite?

 

[Raymont]

The physical significance of the results are not very clear, can anyone explain it?