Limits of integration

In calculus and mathematical analysis the limits of integration (or bounds of integration) of the integral $${\displaystyle \int _{a}^{b}f(x)\,dx}$$

of a Riemann integrable function ${\displaystyle f}$ defined on a closed and bounded interval are the real numbers ${\displaystyle a}$ and ${\displaystyle b}$, in which ${\displaystyle a}$ is called the lower limit and ${\displaystyle b}$ the upper limit. The region that is bounded can be seen as the area inside ${\displaystyle a}$ and ${\displaystyle b}$.

For example, the function ${\displaystyle f(x)=x^{3}}$ is defined on the interval ${\displaystyle [2,4]}$ $${\displaystyle \int _{2}^{4}x^{3}\,dx}$$ with the limits of integration being ${\displaystyle 2}$ and ${\displaystyle 4}$.