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Math Help - An integral question

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    An integral question

    Let f: [a,b] -> R be continuous. Use Riemann's condition and uniform continuity of f to prove that f is integrable.
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    Quote Originally Posted by gasbasis View Post
    Let f: [a,b] -> R be continuous. Use Riemann's condition and uniform continuity of f to prove that f is integrable.
    Start by reading all this: No Title

    A little bit of history is good for the soul.
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    Quote Originally Posted by mr fantastic View Post
    Start by reading all this: No Title

    A little bit of history is good for the soul.

    I am always surprised at your browsing prowess. How do you manage to get not-so-popular but really nice articles? Do you just search for it looking at the question? OR have you read those before and you direct it to people looking for help?
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    Quote Originally Posted by Isomorphism View Post

    I am always surprised at your browsing prowess. How do you manage to get not-so-popular but really nice articles? Do you just search for it looking at the question? OR have you read those before and you direct it to people looking for help?
    Thankyou!

    Usually it's a combination of:

    1. Dumb luck at choosing the correct search string.

    2. Sifting through the hits (which also means moving on to pages 2, 3 .....) until I find something I like.

    Sometimes I'll have it saved as a favorite.

    It's always nice to come across something new, interesting, different or comprehensive.
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    1)Continous functions on closed intervals are uniformly continous.
    2)Let \epsilon > 0 there is \delta > 0 so that |x-y|<\delta \implies |f(x)-f(y)|<\epsilon for all points in interval.
    3)Let P=\{x_0,x_1,...x_n\} be partition with \max (x_{k+1}-x_k) < \delta
    4)Then U(f,P)-L(f,P) (the difference of the upper and lower sums with respect to P) can be made sufficiently small.
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