Now reckon out the area beneath the curve by counting the little squares below the line, from ${\displaystyle x=0}$ as far as ${\displaystyle x=12}$ on the right. There are ${\displaystyle 18}$ whole squares and four triangles, each of which has an area equal to ${\displaystyle 1{\tfrac {1}{2}}}$ squares; or, in total, ${\displaystyle 24}$ squares. Hence ${\displaystyle 24}$ is the numerical value of the integral of ${\displaystyle {\dfrac {x}{3}}\,dx}$ between the lower limit of ${\displaystyle x=0}$ and the higher limit of ${\displaystyle x=12}$.

As a further exercise, show that the value of the same integral between the limits of ${\displaystyle x=3}$ and ${\displaystyle x=15}$ is ${\displaystyle 36}$.

(2) Find the area, between limits ${\displaystyle x=x_{1}}$ and ${\displaystyle x=0}$, of the curve ${\displaystyle y={\dfrac {b}{x+a}}}$.