 The issue of absolute integrability is intricate and depends on whether the Riemann, Lebesgue, or Kurzweil-Henstock (gauge) integral is considered; for the Riemann integral, it also depends on whether we only consider integrability in its proper sense (formula_79 and formula_81 both bounded), or permit the more general case of improper integrals.As a standard property of the Riemann integral, when formula_82 is a bounded interval, every continuous function is bounded and (Riemann) integrable, and since formula_79 continuous implies formula_84 continuous, every continuous function is absolutely integrable.In fact, since formula_85 is Riemann integrable on formula_86 if formula_79 is (properly) integrable and formula_88 is continuous, it follows that formula_89 is properly Riemann integrable if formula_79 is.