So basically the author in question didn't even bother to read the relevant part of the book she referenced, and also misunderstood the explanation of the Area and Integral chapter as something that Irving Alder developed.
I didn't bother looking up the other two references to help preserve my sanity.
> Three formulas have been developed by Alder (3), Vecchio et al. (4), and Wolever et al. (5) to calculate the total area under a curve
[3] Alder I: A New Look at Geometry. New York, The John Day Company, 1966.
This book is in turn available in archive.org:
https://archive.org/details/B-001-001-934/page/n269/mode/2up
So basically the author in question didn't even bother to read the relevant part of the book she referenced, and also misunderstood the explanation of the Area and Integral chapter as something that Irving Alder developed.
I didn't bother looking up the other two references to help preserve my sanity.