Say a particle is moving along a path $\gamma$ in a vector field, then the total work done by the force $\vec{F}$ on the particle is $\displaystyle \int_{\gamma}{\vec F}.d\vec{r}$.
Say if this value where positive what would it mean? Would the particle have expended energy or received energy transferred by the force?
This would belong more in physics stackexchange.
However, your integral means work done by the field, therefore, if it is positive, the field gives the particle energy, and if negative, then the field takes energy from the particle.