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[Community Question] Calculus: Why is $\int_{t_n}^{t_{n+1}} u'(s) ds - u'(t_n) = $\int_{t_n}^{t_{n+1}}(t_{n+1}-s)u''(s) ds$

One of our user asked:

I don't understand why the last step in the following equations is true. Could someone explain this to me please? Don't think context is important here, but just in case it's from a proof of a bound on the error of the explicit Euler method. enter image description here


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