Integration by using derivative

Has anyone seen anything like this before:

lim_(||dx||->0) (sum(k*f'(a+k*dx)*dx^2,k=0..n-1)) = f(b)*(b-a) -
int(f(x),x=a..b)

it looks like a way to integrate a function by using its derivative "in one
go" (instead of having to integrate twice).

I believe theres probably a way to transform it into a riemann integral like
sum but I can't figure out how turn the summand into something like
f(a+k*dx)dx.

Thanks,
AD


.

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