 While it is possible for a discontinuous real function to have an anti-derivative, anti-derivatives can fail to exist even for "holomorphic" functions of a complex variable.For example, consider the reciprocal function, "g"("z") = 1/"z" which is holomorphic on the punctured plane C\{0}.A direct calculation shows that the integral of "g" along any circle enclosing the origin is non-zero.