Given a function ${\displaystyle f\left(x\right)}$ of a real variable ${\displaystyle x}$ and an interval ${\displaystyle [a,b]}$ of the real line, the integral ${\displaystyle {\int }_a^{b}f\left(x\right)dx}$ is equal to the area of a region in the xy-plane bounded by the graph of ${\displaystyle f}$, the x-axis, and the vertical lines ${\displaystyle x=a}$ and ${\displaystyle x=b}$, with areas below the x-axis being subtracted.