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*"If ##f## is continuous on ##[a,b]## and:*

$$g(x) = \int_a^x f(t) dt$$

Then ##g## is continuous on ##[a,b]##, differentiable on ##(a,b)##, and ##g'(x) = f(x)##."

$$g(x) = \int_a^x f(t) dt$$

Then ##g## is continuous on ##[a,b]##, differentiable on ##(a,b)##, and ##g'(x) = f(x)##."

This is the first fundamental theorem of calculus. I'm curious as to why ##g## is only differentiable on ##(a,b)##, but not ##[a,b]##.