Riemann integral

• How to Find the Infimum and Supremum of a Riemann Sum
  For a fixed partition, the infimum and supremum of tagged Riemann sums are the lower and upper Darboux sums; varying partitions changes the answer.
• How to Tell Whether a Function Is Integrable
  On a closed bounded interval, a function is Riemann integrable exactly when it is bounded and its discontinuities have measure zero.