Please see attachment.
Q. Show directly that the function
is integrable on R = [0,1] x [0,1] and find
(Hint: Partition R into by squares and let N , limUp = limLp = integrable
Up = upper Riemann sum of f respect to partition  U(f,p) =
Lp = Lower Riemann sum of f respect to partition  L(f,p) =
Please see the attached file for the full solution.
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is defined as if and otherwise. Show that is integrable on ...
A function is found to be Riemann integrable, and its upper and lower sums are found. The solution is detailed and well presented.