Hey there,

Here's the question:

a.) Prove that if f is integrable on [a,b] and m <= f(x) <= M for all [a,b], then:

$\displaystyle

\int_a^b f(x) dx = (b-a)k

$

for some number "k" with m <= k <= M

b.) Prove that if f is continuous on [a,b], then

$\displaystyle

\int_a^b f(x) dx = (b-a)f(q)

$

for some q in [a,b]

So for the work I set up that U(f,P) - L(f,P) < E, which implies the usualy equasion of the Sum of (Mi-mi)(Change in ti) < E. But I'm unsure where I should start throwing in this "k" variable? Thanks