The Importance of Being Continuous

David Jeffrey
University of Western Ontario, London, Canada

If a function F is the integral of a function f, then F should be continuous on
any interval on which f is continuous.  There are cases, however, in which CAS
return expressions for F which are discontinuous.  If students stumble across
these cases, then they might get incorrect answers to calculations and be
confused.  There are two possible ways to avoid this: explain the danger to the
students, or change the integration algorithms to guarantee continuous
answers.  Both possibilities are discussed.