Explain the difference between the actual definition of a Riemann Integral of function f on the...

Explain the difference between the actual definition of a Riemann Integral of function f on the interval [a,b] and the conclusion of the FTOC Part 2.(Fundamental Theorem of Calculus Part 2)

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Please check the image for complete answer.

I wrote the definition of both Riemann Integral of a function on [a,b] and FTOC Part 2 with necessary conditions in both.

Riemann Integral :- Provides a way to calculate the integral provided the integral exists. (Given function has to be bounded)

Although boundedness doesn't assure you the existence of integral e.g. Dirichlet function.

FTOC :- Assures the existence of integral and give the value of the integral provided the function is continuous on [a,b] and has an anti derivative.

F is anti derivative of f if F' = f.

Colby Messinger answered 1 year ago

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