Boyer 1939 is a nice readable survey of the history of the calculus, but it's showing its age. Discussing the notion of instantaneous velocity, he has:

Mathematics knows no minimum interval of continuous magnitudes [such as distance and time.] Attempts to supply a logical definition of such an infinitesimal minimum which shall be consistent with the body of mathematics as a whole have failed. [p. 7]

This was accurate as of 1939, but is out of date given what we've learned from NSA and SIA. Boyer's account reads somewhat as the glorious march to victory of the limit concept.

Bell 2005 is more modern, but a review by Ehrlich (can't find a reference, but the text comes up in google) complains that it comes off as a sales job for SIA. (It's also extremely expensive.)

Is there a modern source on this topic that doesn't have an ax to grind?

Bell, The continuous and the infinitesimal in mathematics and philosophy, 2005.

Boyer, The History of the Calculus and its Conceptual Development, 1939. https://archive.org/details/TheHistoryOfTheCalculusAndItsConceptualDevelopment

related:

everyonehas an ax(e) to grind... $\endgroup$ – Yemon Choi Jun 7 '14 at 2:49