All these calculations are actually integrals (calculating areas below any curve within a certain range) with a lot of variables, but if you read the text in the link, posted by eKretz, that talk about how to derive from the original formula, you can clearly see that most components cancel out. This is why the formulas become what they are.
About graphing calculators...I bought a TI-85 when I was in high-school. Many of my friends had HP or Casio, except one who also had TI-85. We were the only ones who could calculate any problem that was given to us, using the calculator only. All others had issues because there was something always missing. :-) TI series calculators are really good, and they have pretty much everything, but the formulas and constants for certain things can be found under unexpected menus. But once you understand how the calculations are done, one can find everything needed to get the right answer from one single equation. :-)
Love TI, and don't like the other brands that much. Not bad calculators, but for me they just don't make any sense at all. Casio and HP had a lot of features that TI did not have, but for pure Math, Chemistry and Physics problems those features were of no help to solving the problem.