Integral
Let f:[a,b]→R and g:[a,b]→R be two bounded functions.Suppose f≤g on [a,b]. Use the information to provethatL(f)≤L(g)andU(f)≤U(g).
Information:
g : [0, 1] —> R be defined by ifx=0, g(x)=1; if x=m/n (m and n are positiveinteger with no common factor), g(x)=1/n; if xdoesn't belong to rational number, g(x)=0
g is discontinuous at every rational numberin[0,1].
g is Riemann integrable on [0,1] based on the fact thatSuppose h:[a,b]→R is continuous everywhere except at a countablenumber of points in [a,b]. Then h is Riemann integrableon[a,b].
f : [0,1]→R deï¬ned by (f(x) =0 if x =0) and (f(x)=1 if 0 < x≤1)
f is integrable on [0,1]
