Why is $\int -\frac{1}{\sqrt{1-x^2}} dx = -\arcsin(x) $ and not $ \arccos(x) $

Question

I'm currently learning calculus on my own, and I have started to meet integrals with arcsin(x) and arccos(x). According to the book I'm using $\frac{d}{dx}(\arccos(x))=-\frac{1}{\sqrt{1-x^2}}$. However, everywhere else, I see: $$\int -\frac{1}{\sqrt{1-x^2}} dx=-\arcsin(x) $$Why is $\int -\frac{1}{\sqrt{1-x^2}} dx≠\arccos(x) $? Help would be much appreciated.

Answer 1

You're missing the constant of integration, which solves the issue. So both are correct, since

$$\arccos(x)=-\arcsin(x)+\frac{\pi}{2}.$$