Answer to Question #95945 in Calculus for Rachel

Question

A comparison between the Darboux-integral and the Riemann-integral.

Answer 1

The main difference between the Riemann integral and the Darboux integral is that in the Riemann integral the integrand defined for a given integral is calculated by splitting it into a set of rectangles and in the sum of their areas, in the Darboux integral there is an upper value of the integral and a lower one. And if the function is integrable, then the lower Darboux integral is equal to the upper Darboux integral and is equal to the Riemann integral.