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Riemann integral problem

  1. May 7, 2010 #1
    suppose f and g are bounded functions on [a,b] such that f+g is in R[a,b]

    Then, does it follow that f and g are also in R[a,b]? i wanto to prove whether it is or not
  2. jcsd
  3. May 7, 2010 #2


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    Not so. Let f be a function which is NOT Riemann integrable and let g=1-f.

    For example f(x)=1, when x is irrational and f(x)= 0, when x is rational.
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