If $\vec F$ is a path-independent vector field, with $\int_{(0,0)}^{(0,1)}\vec F \cdot d\vec r = 4.4$ and $\int_{(0,1)}^{(1,1)}\vec F \cdot d\vec r = 3.2$ and $\int_{(1,0)}^{(1,1)}\vec F \cdot d\vec r = 3.3$, find $$\int_{(0,0)}^{(1,0)}\vec F \cdot d\vec r.$$

$\int_{(0,0)}^{(1,0)}\vec F \cdot d\vec r =$