(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the integral from 0 to x of (sin t)/(t + 1) dt > 0.

(Sorry I don't know how to use the integral latex.)

2. Relevant equations

We have only learned about lower and upper sums, and how the integral is equal to the supremum of lower sums and the infimum of upper sums when sup = inf

3. The attempt at a solution

I took a partition from 0 to x with equal intervals, so that each interval has length x/n for n intervals. I found the lower sum and upper sum, with a difference of x/n * (sin x)/(x + 1). I have no idea what to do afterwards. Am I to eliminate the possibility of the integral being 0 and negative?

EDIT: I "found" the lower and upper sums incorrectly - in fact, they are not possible to determine.

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# Proving Positive Integral using Sums

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