I found no way to rescue the cumulative f(x) as given.
It must be reconstructed wrt scalar exp(x), ln(x) as indicated.
Result above max ... otherwise can't calculate.
Pure didactic for the unexpected red.



Integral 0Discrete Cumulative.sm (31 KiB) downloaded 63 time(s).

Wrote

I found no way to rescue the cumulative f(x) as given.
It must be reconstructed wrt scalar exp(x), ln(x) as indicated.
Result above max ... otherwise can't calculate.
Pure didactic for the unexpected red.

Here is the scalar reconstruction ... two same plots.
Bad luck: native Smath Simpson integrator is inadequate.
In any cases of integration, always wise to sanity
cumulative integration from FD [Finite Differences].
The simplest FD in this forum has been tested exhaustively
vs more advanced FD [F.B. Hildebrand] ... not to avail.
Considering noisy data sets, unless you can declare the
model fit function exact: FD will integrate the noisy
data set very closely true, directly from the noisy set.

Integral 0Discrete Cumulative [Simpson freak].sm (15 KiB) downloaded 65 time(s).