The curve $y = x ^ { 3 } - 6 x + 3$ has turning points at $x = \alpha$ and $x = \beta$, where $\beta > \alpha$.
Find
$$\int _ { \alpha } ^ { \beta } x ^ { 3 } - 6 x + 3 \mathrm {~d} x$$
A $- 8 \sqrt { 2 }$
B - 10
C $- 10 + 6 \sqrt { 2 }$
D 0
E $\quad 12 - 8 \sqrt { 2 }$
F $\quad 6 \sqrt { 2 }$
G 12