Complex Analysis, Line Integrals and Cauchy Conceptually

[jmm5872]

I am just trying to get the conceptual basics in my head. Can I think of things this way...

If you are taking the integral of a function f(z) along a curve γ in a region A. If the curve is closed and f(z) is analytic on the entire curve as well as everywhere inside the curve, then the integral is zero.

Is this basic statement always true?

 

[Dick]

Yes, that's always true.