Answer to Question #20053 in Real Analysis for Matthew Lind

Question #20053
Consider the function on [1,5]: f(x) = 1, x=2 -3, x=4 0, x element of [1,5], x not equal to 2, x not equal to y. a) Show that for every epsilon greater than 0 there exist a partition P_epsilon of [1,5] such that L(f, P_epsilon) > -epsilon, and partition Q_epsilon of [1,5] such that U(f, Q_epsilon)< epsilon. b) Based on part a, prove that f is Reimann integrable on [1,5] and compute the integral.
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