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https://gyazo.com/92d834eb3c6b3c500bda5cf7e2d68fc2

I just used the definition.

$$\bigg|\lim_{n\to\infty} \sum_{i=1}^{n} f(x_i^*)\Delta x\bigg| \leq \lim_{n\to\infty} \sum_{i=1}^{n} |f(x_i^*)|\Delta x$$ by def

idk what to do. Hints?

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    Basically, you are done. – 2017-02-14
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    This question is taken from a past midterm question which is out of like 70. I'm having a hard time believing that this answer would give me 10% of that exam. :/. Btw do you know how to paste images like without having to click on it and it just shows. – 2017-02-14
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    Your answer is not rigorous, but heuristically correct. – 2017-02-14
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    I just applied the definition :O . Is there nothing more I should do? An explanation maybe – 2017-02-14
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    I don't think the above would make the cut in a slightly more strict school. Perhaps it was expected something like: using the triangle inequality, we know that $$\left|\sum_{i=1}^n f(x_i)\Delta_{x_i}\right|\le\sum_{i=1}^n |f(x_i)|\Delta_{x_i}\$$ so when taking the limit when $\;n\to\infty\;$ while $\;\sup\left\|\Delta_x\right\|\to 0\;$, the inequality still is true as we know from sequences and their limits. Q.E.D. – 2017-02-14
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    $− |f(x)| ≤ f(x) ≤ |f(x)|$ holds for all x ∈ dom(f). I was thinking showing that – 2017-02-14

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