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If I take the indefinite integral for sin(x) on Desmos, why do I get this graph

https://www.desmos.com/calculator/zqpbtac8az

instead of a graph of -cos(x)?

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    $\begingroup$ note that you're integrating $\sin(x)$ with respect to $t$. $\endgroup$ – Scounged Jan 21 '18 at 20:41
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The integral is with respect to $dt$, so only $t$ varies over the integral, but you've integrated $\sin x$, not $\sin t$. Try changing it to $\sin t$.

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  • $\begingroup$ Oops, my bad, should have paid more attention, thank you both. $\endgroup$ – Aremus Jan 21 '18 at 20:50
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Waht you have is $$\int_0^{\color{red}{x}} \sin \color{red}{x}\,\mathrm d t=x\sin x.$$

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