$\textbf{I would like a proof in detail of the following question.}$ 

let $ f:[a,b)\rightarrow \mathbb{R} $ be a bounded function which is Riemann integrable on [a,c] whenever $a< c< b$. Define the function $F:\left[ a,b\right)\rightarrow \mathbb{R} $ by the formula $F(x)=\int_{a}^{x} f$Prove that $F$ has a limit at $b$ and the integral of $f$ over $[a,b)$ can be defined to equal this limit.

Answer

Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.