1. ## simple integral questions

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)?

2. Take $f(x)= \frac{1}{2(b-a)}$ and $g(x)= \frac{2}{b-a}$ if $x\in \left[ a,a+\frac{b-a}{2} \right]$ and $g(x)=0$ otherwise then $\int_{a}^{b} f=1/2 \leq 1=\int_{a}^{b} g$ but $f\nleq g$.

For the second one assume $f(x) > g(x)$ for all $x$ and use that the integral is monotonic (ie. preserves inequalities)