The diagram shows the curve \(y=12+x-x^2\) intersecting the line \(y=x+8\) at the points \(A\) and \(B\).

(i) Find the coordinates of the points \(A\) and \(B\).

(ii) Find \(\displaystyle\int(12+x-x^2)\,dx\).

(iii) Showing all your working, find the area of the shaded region.