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**0123** sorry for posting another question but I have a class test and I'm getting full of doubts.. ok, the definition of integral by Riemann that I've studied is(I know you know it): let f bounded on (a;b), f is integrable on (a,b) if the upper and lower sum's limits converge to the same finite number.

then should it be true that

if f(x) is bounded on (a,b) then it is integrable according to Riemann?..

the book says that if F(x) is continuous it is integrablle on (a,b) according to Riemann.

thanks a lot