We will discuss the properties of a family of integrals involving the cardinal sine function, first studied by Borwein \& Borwein. The aim is to provide a physicist's perspective onto a curious change of behaviour occurring within this family, noticed when benchmarking computer algebra packages, and initially attributed to a bug. A number of non-trivial generalizations will be obtained in a calculation-free way. \\ \\Work in collaboration with Satya Majumdar \\ \\ (On-Line Seminar, link sent by email. For inquiries: marco.schiro@ipht.fr)