Holomorphic function on the complement of an interval [duplicate]

Suppose $f : \mathbb{C} \to \mathbb{C}$ is continuous and its restriction to $\mathbb{C} \setminus [-1,1]$ is holomorphic. Is $f$ necessarily holomorphic?

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marked as duplicate by Jonas Meyer, JSchlather, 5PM, Henry T. Horton, PaulJan 22 '13 at 2:20

This question was marked as an exact duplicate of an existing question.

Yes – user53153 Jan 22 '13 at 0:52
@5PM: I saw that post, but it looked much more advanced and I incorrectly assumed that it wouldn't contain a solution to my simple problem. Thanks for pointing this out. – Justin Campbell Jan 22 '13 at 1:34
Others: math.stackexchange.com/questions/170821/… and math.stackexchange.com/questions/202887/… (for which answers weren't posted). – Jonas Meyer Jan 22 '13 at 2:00