The first formula is just standard formula for integration along a non-closed path- a path that has two distinct endpoints.

Green's theorem and Stoke's theorem are almost the same- Green's theorem applies to a closed path in the xy-plane, Stoke's theorem to a closed path in three dimensions.

The divergence theorem has nothing to do with "paths". It relates the integral on a closedsurfaceto the integral over the region inside that surface.