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Suppose $f$ is analytic on the domain $D = \{z \big| |z|>1\}$ in $\mathbb{C}$. I know that if the line integral of $f$ along any closed path is 0 then $f$ has an anti-derivative. Is this also a necessary condition.

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    Oh, oops, read the inequality the other way. You really shouldn't use $D$ for a domain that is not a disk :p (Though steps used in the *proof* of Cauchy-Goursat will also give you what you want, like Jonas' answer below.)2010-12-17

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Yes. If F'=f and $\gamma:[a,b]\to D$ is a curve, then $\int_\gamma f = F(\gamma(b))-F(\gamma(a))$. For example, see Theorem 1.18 on page 65 of John B. Conway's Functions of one complex variable.