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I am a newbie and this is my first post in PF. I have recently started on learning calculus and I'm using Apostol's calculus-I (second edition). I need some clarification on "The method of exhaustion for the area of a parabolic segment" (I 1.3 page 3). I'm able to follow the author till equation I.4 in page 6. After that there is a statement "For our purposes, we do not need the exact expressions given in the right-hand members of (I.3) and (I.4). All we need are the two inequalities" and there is equation - I.5 after that. Can someone explain me the reason how one can obtain equation I.5 (the inequality equation)?

Thankyou for reading my post

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# Clarification on a topic in Apostol's calculus text

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