In this lecture we work to determine which functions are Riemann integrable. We will prove that all continuous functions on a closed and finite interval are integrable, showing that the vector space of continuous functions is a subset of the vector space of Riemann integrable functions. We further show that there are functions that are not continuous that are Riemann integrable by proving that all monotone functions are integrable. We then conclude the lecture by providing a useful variant of the Darboux integrability condition which is significantly easier to apply than the condition presented in the previous video lecture.
This course is taught by Jason Bramburger.
