I have a problem that gives me a M.G.F and asks for P(1< or = X < or = 2)

For example M(t)= $\displaystyle (0.3 + 0.7 e^t)^5$

P(1< or = X < or = 2) = 0.1607

How is that done? I can't find the principle in my text.

I know that P(2) is equal to M(2) but how about the above example ?

Edit: If possible please post a link to a a page that explain how to use M.G.F , I'm having problems with various applications. Like how to get the M.G.F from E(X).