5.
The curve with equation \(y = x ^ { 3 } - 7 x + 6\) is sketched below.
\includegraphics[max width=\textwidth, alt={}, center]{a1b449df-1096-4b3a-8306-fca410a7e530-10_428_627_342_810}
The curve intersects the \(x\)-axis at the points \(A ( - 3,0 ) , B ( 1,0 )\) and \(C\).
- Find the coordinates of \(C\).
[0pt]
[1 mark] - Find \(\int \left( x ^ { 3 } - 7 x + 6 \right) \mathrm { d } x\)
[0pt]
[2 marks] - Find the total area of the shaded regions enclosed by the curve and the \(x\)-axis.
[0pt]
[4 marks]