a) Prove that for each n N is a partition of [0, l ]. b) Prove that a bounded function f is integrable on

a) Prove that for each n ˆˆ N

is a partition of [0, l ].
b) Prove that a bounded function f is integrable on [0,1] if

in which case ˆ«10 f(x)dx equals I0.
c) For each of the following functions, use Exercise 1.4.4 to find formulas for the upper and lower sums of f on Pn, and use them to compute the value of ˆ«10 f(x)dx.
α)f(x) = x
β)f(x) = x2

) f(x)=11 1/2 151