The Fundamental Theorem is "fundamental" because it links the two distinct branches of calculus, derivatives and integrals. As you can see above, it is split into two parts.

Here's what I mean by "take it-stick it-D it". Look at this example, first:

/\ u(x)
d |
-- | f(t) dt
dx |
\/ a

Taking-sticking-D-ing is a phrase that was "patented" by my high school math teacher, Mr. Noeth. In this example, t is the variable of integration. To T-S-D, you take that end limit ("take it"), replace the variable of integration with it ("stick it"), and take the derivative WRT x of it ("D it"). So you have:

du
f(u(x)) * --
dx

Note that you can use any variables, not just x and t.