1. Let f be bounded and integrable on [a,b]. Define the partition PN = {a, at N, ba .at(6-a . by, the division of b,a into N equally sized intervals. Let Ci= at i( 6-a) n be the right endpoint of the jth in- terval, and define the right Riemann sum RN(f) = Eif(x;). a). Show that for any N, we have LPN (f) LPN (f) > LP(f). c). Con- clude that limN-> LPN (f) and limN- UPN (f) both converge to f f(x)dx. d). Use the squeeze theorem to see that limN- RN(f) = S. f(x)dx