This is one of those topics which varies widely from school to school. Different units, different formulas... It's a mess. It's physics. And many teachers don't even cover it in calculus. So watch the videos below with an eye towards your notes: if your teacher doesn't do them the way I do in the videos, or the problems are worded different, you want to make sure you know how to do them your teacher's way too.
Intro to Pressure: Concepts, Formulas & Units
This video introduces the concept of pressure and its basic formula, P=F/A. It also explains what units to use with pressure, how to convert bad units into good units, and how to do basic calculations where a problem is asking for pressure or force due to a pressure.
Pressure & Force Due to Depth
This video explains why the pressure changes as we go up and down in the ocean or atmosphere, and it explains how to calculate the pressure at a given depth. It then gets into calculating the force on submerged windows and surfaces, and goes over some trick questions that teachers can try to burn you with. Example: If atmospheric pressure is 14 pounds per square inch, why isn't your kitchen table crushed?
Using Integrals to Calculate Pressure Force
Finally, what we've been building up to: using integration to calculate the force due to pressure and depth! These are tough to set up, but if you've already watched the non-calculus pressure videos they shouldn't completely blow your mind. They also bear a striking resemblance to area and centroid problems, so at least the integrals here should seem eerily familiar...
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)