The graph of $y=f^{\prime }\left(x\right)$, 0 ≤ $x$ ≤ 5 is shown in the following diagram. The curve intercepts the $x$-axis at (1, 0) and (4, 0) and has a local minimum at (3, −1).

The shaded area enclosed by the curve $y=f^{\prime }\left(x\right)$, the $x$-axis and the $y$-axis is 0.5. Given that $f\left(0\right)=3$,

The area enclosed by the curve $y=f^{\prime }\left(x\right)$ and the $x$-axis between $x=1$ and $x=4$ is 2.5 .