I've been working with bounding the Taylor error by integrating and I note that it seems to be standard in many texts (including Hughes/Hallet) to write something of the form int(f '(x),x,a,x) instead of int(f '(t),t,a,x); that is, foregoing the "correct" practice of using a different (dummy) variable for integration as opposed to the upper bound of integration.
The problem seems to be that with multiple integration you need a different dummy variable at each stage, making the notation awkward.
Is there a better way? Does it matter? Is this a dumb question? Is there a dummy answer?
PS Got a gut level, intuitive interpretation of the error you'd care to share?