6 The curve with equation \(y = x ^ { 3 } - 2 x ^ { 2 } + 3\) is sketched below.
\includegraphics[max width=\textwidth, alt={}, center]{c44c229e-44b2-4799-9c9c-bfccdd09d450-4_590_787_365_625} The curve cuts the \(x\)-axis at the point \(A ( - 1,0 )\) and passes through the point \(B ( 1,2 )\).

1. Find \(\int _ { - 1 } ^ { 1 } \left( x ^ { 3 } - 2 x ^ { 2 } + 3 \right) \mathrm { d } x\).
   (5 marks)
2. Hence find the area of the shaded region bounded by the curve \(y = x ^ { 3 } - 2 x ^ { 2 } + 3\) and the line \(A B\).
   (3 marks)