The diagram shows part of the curve \(y = -x^2 + 8x - 10\) which passes through the points \(A\) and \(B\). The curve has a maximum point at \(A\) and the gradient of the line \(BA\) is 2.

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

(ii) Find \(\int y \, dx\) and hence evaluate the area of the shaded region.