With this chapter starts the process of renormalization, how to assign in a consistent way a finite value to all these diverging integrals. The procedure itself is fully rigorous. It is the fact that the result of this procedure brings us information about the physical world which is largely an act of faith (which is however supported by experimental data to an astonishing degree of precision). We perform preliminary work, giving necessary conditions for rational functions to be integrable by comparing the degrees of the numerator and denominator, conditions which turn out to be sufficient for the rational functions of interest in computing the values of Feynman’s diagrams, a result known as Weinberg’s power counting theorem.