Fundamental Theorem of Calculus

FTC states the existence of the integral;
Integral[f(x)dx,a,b] = F(b)-F(a)
An iteration of FTC gives Taylor's expansion and maps e^z to polynomials;
e^z = Sum[z^n/n!, n=0,...,Infinity]
The weighing factor 1/n! diminishes the higher polynomials and ensures absolute convergence.
It reminds the number of states of ESet;
SEn = n!(n-1)!(n-2)!...1!0!
ESet is derived from iterating a simple operation, like the e^z sum.
Then one would expect the Integral[] definition to be like the ESet operator E.
ESet accumulates its past and determined uniquely by its initial and final states, like Integral[].
ESet seems isomorphic to e^z.