# Limits of integration

In calculus and mathematical analysis the limits of integration of the integral

$\int_a^b f(x) \, dx$

of a Riemann integrable function f defined on a closed and bounded [interval] are the real numbers a and b.

## Improper integrals

Limits of integration can also be defined for improper integrals, with the limits of integration of both

$\lim_{z \rightarrow a^+} \int_z^b f(x) \, dx$

and

$\lim_{z \rightarrow b^-} \int_a^z f(x) \, dx$

again being a and b. For an improper integral

$\int_a^\infty f(x) \, dx$

or

$\int_{-\infty}^b f(x) \, dx$

the limits of integration are a and ∞, or −∞ and b, respectively.