What is wrong with the following statement:
Let f(x) be Riemann-integrable, F(x)=∫xaf(t)dt. Then F(x) is differentiable, and F′(x)=f(x) almost everywhere.
I think the statement is true. Because f(x) be Riemann-integrable, it's continuous almost everywhere. Then by the Second Fundamental Theorem of Calculus, F(x) is is differentiable almost everywhere, and F′(x)=f(x) almost everywhere.
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