Darboux integral

Summary

The Darboux integral defines the integral of a bounded function on a closed interval by squeezing it between upper and lower Darboux sums. A function is Darboux integrable when its upper and lower Darboux integrals agree, and the integral is the common value. This gives exactly the same integrable functions and the same values as the Riemann integral, by a classical theorem. It is often the most convenient way to prove that a given function is integrable.