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Can you help me prove this?

Suppose that f:[a.b] -> R is integrable and that F:[a,b]->R is a differentiable function such thet F'(x)= f(x) for all xLaTeX Code: \\in [a,b].

Prove from the definition of the integral that;

F(b)-F(a) =LaTeX Code: \\int f(x) dx ( integral going from a to b)

I can prove this using the Fundamental theorem of calculus;however, this question specifically asks that we use the definition of integral to prove this:

I'm thinking that I have to use the "partition" prepositions to prove this.

Any ideas?

Thank you in advance guys!

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# Proving F'(x)= f(x) using the definition of integral?

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