Riemann integral

Darboux integrals have the advantage of being simpler to define than Riemann integrals.

The most commonly used definitions of integral are Riemann integrals and Lebesgue integrals.

In some cases such integrals may be defined by considering the limit of a sequence of proper Riemann integrals on progressively larger intervals.

Darboux integrals are equivalent to Riemann integrals, meaning that a function is Darboux-integrable if and only if it is Riemann-integrable, and the values of the two integrals, if they exist, are equal.