Integral of sin(x) problem.

Question

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)?

Answer 1

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 $\sin t$.

Answer 2

Waht you have is $$\int_0^{\color{red}{x}} \sin \color{red}{x}\,\mathrm d t=x\sin x.$$