True or False. Prove if they are true or false or give a counterexample:
1.Let F be a function of bounded variation on [a,b] such that F'(x) = 0 almost everywhere.
Then F is constant.
2.If f is an analytic function the annulus U = {z E C : 1 < Iz| < 4}, then f has an antiderivative in U
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