In this paper the regularization of functions and improper integrals is analyzed. Some definitions based on Hadamard's finite part method and Gel'fand-Silov's regularizations are compared and another modification of Hadamard's finite part is used. In particular, it turns out that this regularization and type II Gel'fand-Silov regularization (see below) are consistent on a rather wide set of (in general) non-integrable functions.