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Calculus/The continuity of the integral

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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.

Answer
Yes, integration is a "smoothing" process.

Check these:
http://www.physicsforums.com/showthread.php?t=358567
http://www.math.ku.edu/~lerner/m500f09/Integration%20theory.pdf
http://en.wikipedia.org/wiki/Continuous_function#Relation_to_differentiability_a

Abe

Calculus

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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