Answer
$\mathop \smallint \limits_C {\bf{F}}\cdot d{\bf{r}} = 6$
Work Step by Step
From Figure 17 we see that $f\left( Q \right) = 8$ and $f\left( P \right) = 2$.
By Theorem 1:
$\mathop \smallint \limits_C {\bf{F}}\cdot d{\bf{r}} = f\left( Q \right) - f\left( P \right) = 8 - 2 = 6$