Integration -- basic problems

I don't think I really understand what I am doing. This topic has me a little befuddled, so please bear with me.

First, how do you correctly express the integration of a constant? (And no, my text does not explain this. I have looked several times.)

As in:

$\displaystyle \int_{-3}^{-1}5dx$

I understand that the answer is 10 (the area bound by the lines $\displaystyle y=5, y=0, x=-1$ and $\displaystyle x=-3$) but not how to obtain or express that answer using the definite integral.

$\displaystyle \int_{a}^{b}f(x)dx=\lim_{\|P\|\to0}\sum_{k=1}^{n}f (x_{k}^{*})\Delta x$

Does not seem to make sense when f(x) is a constant.

Thanks for the help! Integration may be my waterloo.