A gardener lays out a flower bed on level ground…

Step 1. Meeting points. $5x - x^2 = x$ gives $x^2 - 4x = 0$, so $x = 0$ or $x = 4$.

Step 2. Which is above? At $x = 2$ the curve gives $6$ and the line gives $2$, so the curve is above.

Step 3. The area. $\displaystyle\int_0^4 (4x - x^2)\,dx = \left[2x^2 - \dfrac{x^3}{3}\right]_0^4 = 32 - \dfrac{64}{3} = \dfrac{32}{3}$.