Extrapolated Faá Di Bruno's Formula

[Xorter]

Here is how to evaluate the nth derivative of f o g:
https://en.wikipedia.org/wiki/Faà_di_Bru...orial_form
http://www.maa.org/sites/default/files/i...17-234.pdf
My question is that: Is it possible to get a formula for integrate f o g dx? Where integrating means the -1st derivative.
Can we extrapolate this formula to the negative numbers?

[Xorter]

What if I say the next:
N=-1
int f o g dx = ?
-1b[-1] = -1
b[-1] = 1
k = 1
int f o g dx = (-1)!/1! f' o g * (g^(-1)/(-1)!)^1 = f' o g * int g dx

But it does not work ... Why?