Suppose [itex]f : \mathbb{C}\to \mathbb{C}[/itex] is continuous everywhere, and is holomorphic at every point except possibly the points in the interval [itex][2, 5][/itex] on the real axis. Prove that f must be holomorphic at every point of C.
How can I go from f being holomorphic every except that interval to showing it is holomorphic at that interval? I am assuming it has to be due to continuity.
But there are continuous functions that aren't differentiable every where.
