What goes up has to stop before coming down (max/min)

The whole is the sum of the parts (integrals)

The whole change is the sum of the partial changes (the fundamental theorem)

One variable at a time

Everything in Calculus is based on the idea of limits. We figure things out by getting an approximate answer $a_1$, then a (hopefully better) answer $a_2$, then another answer $a_3$. If we're lucky, the limit of this sequence of approximations is our true answer.