User:Keith.U/Sandbox/Riemann Integral

Definition
Let $\left[{a \,.\,.\, b}\right]$ be a closed real interval.

Let $f: \left[{a \,.\,.\, b}\right] \to \R$ be a real function.

Darboux's Definition
More usually (and informally), we say:
 * $f$ is (Riemann) integrable over $\left[{a \,.\,.\, b}\right]$.

Also known as
Darboux's definition of the Riemann integral is also known as the Darboux integral for.

Many sources whose target consists of students at a relatively elementary level refer to this merely as a definite integral.

Also see

 * Definition:Riemann Sum
 * Definition:Signed Area
 * Continuous Real Function is Darboux Integrable


 * Equivalence of Definitions of Riemann Integral

There are more general definitions of integration; see:
 * Definition:Lebesgue Integral
 * Lebesgue Integral is Extension of Riemann Integral