  This paper offers what seems at first to be a minor technical correction to
the current practice of computing indefinite integrals, and introduces the idea
of a "Kahanian constant of integration". However, the total impact of this
minor correction is potentially large because the current practice is taught
early at the university level and to very many students---most of whom do not
go on to become mathematics majors. Moreover, computer algebra systems have
become widespread, including good free ones, some of which are available for
smartphones. Most current computer algebra systems apply current textbook rules
and amplify the effects of fundamental "minor" errors such as the error in
continuity that we address in this article. So in practice, the correction we
present is important.
