Riemann integrable functions
PLease, help
If $f(x)\leq g(x)\forall x\in [a,b]$. There exist $x_0$ such that $f(x_0)

Question

Riemann integrable functions
PLease, help
If $f(x)\leq g(x)\forall x\in [a,b]$. There exist $x_0$ such that $f(x_0)<g(x_0)$
i)True or False 
$$\int_a^b f(x) dx <\int_a^b g(x) dx$$
ii) Now, Suppose f, g are continuous on [a,b] , prove 
$$\int_a^b f(x) dx <\int_a^b g(x) dx$$

chaise · Answer

I am pretty sure the answer is true, but I have no idea how to prove it.