Tutorial on loop integrals which need regularisation but yield finite results

In this pedagogical note I will discuss one-loop integrals, where (i) different regions of the integration region lead to divergences and (ii) where these divergences cancel in the sum over all regions. These integrals cannot be calculated without regularisation, in spite of the fact that they yield a finite result. A typical example where such integrals occur is the decay H --> gamma gamma.