Definition (Definite Integral): Let be continuous on the closed interval

Remark: If on , then can be thought of as an approximation to the area under the curve of f from to
Def: Let f be a function bounded on . We say that f is Riemann integrable over if there exists a real number such that for every partition and any choice of , we have

²

In this case, we say exists, write and denote by called the definite/Riemann integral of f over .

The components that make up the Definite/Riemann Integral are named as follows:

Upper Limit of Integration

Integrand



Integral Sign

Variable of Integration

Lower Limit of Integration