http://www.askamathematician.com/20...gralantiderivative-the-area-under-a-function/(adsbygoogle = window.adsbygoogle || []).push({});

this website says

f^\prime (c) (B-A) = f(B)-f(A) or f(c) (B-A) = F(B)-F(A) (since F’ =f).

but seems like this is wrong. because B-A= Δ x,

f'(c)*Δ x= Δy

and the area might be Δx*f(c).

Can anyone give me proof or link that explains this throughly?

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# Integral, why antiderivative is area under curve

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