strange partial integration

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I was reading a solution to calculating some integral. one of the steps is:

$$\int xe^{-x^2}\sin(ax) dx = -\frac{1}{2}\int \sin(ax) de^{-x^2}$$

I am not familliar with the notation $de^{-x^2}$ because I normally use $du$ and write $u=....$. But in this case I understand it.

Now the next step I dont get:

$$\int \sin(ax) de^{-x^2}=-\int e^{-x^2} d\sin(ax)$$

What happens here?? I can't get the substitution $u=, du=...dx$ steps clear to do it myself