Originally Posted by

**serious331** Suppose that two bounded functions $\displaystyle f : [a,b] \rightarrow R$ and $\displaystyle g : [a,b] \rightarrow R$ have the property that $\displaystyle g(x) \leq f(x)$ for all x in [a,b].

For a partition P of [a,b] show that $\displaystyle L(g,P) \leq L(f,P)$

I tried to do this by considering a partition $\displaystyle P = \{{x_0},...{x_n}\}$, and for each index $\displaystyle i \geq 1$, the number m is a lower bound for both the functions given x in $\displaystyle [{x_i-1}, {x_i}]$. so, $\displaystyle m \leq m_i$

is this the correct path? I am stuck on this step..