Help in understanding the proof of the Principle of deformation of paths I am studying the book "Complex variables and applications" by James Ward Brown, Ruel Vance Churchill and I don't understand the proof given in the text.
The proof uses a theorm:

Proof:

How can we apply the theorm ? isn't $-C_1$ and $C_2$ in different orientation (in terms of clockwise direction) so we can't apply the theorm ? 

By definition, the line integral changes sign when you "negate" the contour (change its orientation)
