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If $f:\mathbb{R}\to \mathbb{R}$ and $f(x)=0$ if $x\in \mathbb{Z}$ and $f(x)=x-\lfloor x\rfloor-\frac12$ if $x\in \mathbb{R}-\mathbb{Z}$. Let $A(x)=\int_0^x f(t)\mathrm dt$.

Show that $A(x)=\dfrac{x^2-x}{2}$ if $0\leq x\leq 1$.

I am supposed to use the definition of Riemann Integral.

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    Did you notice that $x \in \mathbb Z$ only at $x = 0$ and $x = 1$ in your domain?2011-10-19
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    @JonasTeuwen Yeah I have some other things to prove in my homework assignment so it's useful for that part.2011-10-19
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    Well then, what does $[x]$ mean to you?2011-10-19
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    [x] denotes the greatest integer less than x.2011-10-19

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