Can some one explain what is independent of choice of representation means

if curl of F is zero then line integral independent of path.....but if curl of F is non zero than line integral depands on path

Here C1 and C2 are two different path but have same starting and ending points . So , it's saying that if start-end point are same doesn't imply that line integral along c1 and ...

is line integral independent of path are dependent of path