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# Calculus/The integral of a continuous function

Question
Hi,
let f be a continuous function on the interval (a,b)
then is the integral of f between x0 and x, where both x0 and x are in (a,b), also continuous on (a,b)?

Please direct me to an internet reference that answers the question, or simply just supply me with an answer.

Thanks for your time.

If a function is continuous on (a, b), then the integral is also continuous on (a,b).
In the proof of continuity of a function, there was a statement that for any d small enough,
there existed an e such that |f(x+a)-f(x)| < e if |a|<d.

This same thing can be applied if we take e*f(x) at the point in question.

Calculus

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