The diagram shows part of the curve \(y=x^3+4x^2-5x+5\) and the line \(y=5\).

The curve and the line intersect at the points \(A\), \(B\) and \(C\).

The points \(D\) and \(E\) are on the \(x\)-axis and the lines \(AE\) and \(CD\) are parallel to the \(y\)-axis.

(i) Find \(\int(x^3+4x^2-5x+5)\,dx\).

(ii) Find the area of each of the rectangles \(OEAB\) and \(OBCD\).

(iii) Hence calculate the total area of the shaded regions enclosed between the line and the curve. You must show all your working.