Let $f ( x )$ be a real-coefficient cubic polynomial. The function $y = f ( x )$ has a local minimum at $x = - 3$ and a local maximum at $x = 1$. Given that the slope of the tangent line at the inflection point of the graph of $y = f ( x )$ is 4, so that $f ^ { \prime } ( x )$ is as found in question 14.
Find the value of $\int _ { - 3 } ^ { 1 } f ^ { \prime } ( x ) \, d x$.