3.88: Area between a cubic curve and a horizontal line

The diagram shows part of the curve $y = (x - 9)(x - 3)$ and the line $y = 3 - k$, where $k > 3$. The line through the maximum point of the curve, parallel to the $y$-axis, meets the $x$-axis at $A$. The curve meets the $x$-axis at $B$, and the line $y = 3 - k$ meets the curve at the point $C(k, 3 - k)$.