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

\int _{{-\infty }}^{b}f(x)\,dx

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