Why keep doubling the segments for an automatic integrator based on Trapezoidal rule?

Automatic Integrator
Automatic Integrator
Automatic Integrator
Automatic Integrator

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://www.youtube.com/numericalmethodsguy.  

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