Take and if and otherwise then but .
For the second one assume for all and use that the integral is monotonic (ie. preserves inequalities)
These questions are stumping me for some reason, they seem simple yet I cant figure it out:
Let f,g be riemann integrable such that int(a,b)(f) <= int(a,b)(g)
where int(a,b) is the integral from a to b.
is it true that f(x) <=g(x) for all x in [a,b]?
is it true that there exists c in [a,b] such that f(c) <= g(c)?