How does this integral change due to restricted x values?

Question

So, I integrated this integral: $$I = \int\frac{dx}{(x^2+4)\sqrt{1-x^2}}$$ And got: $$I = \frac{1}{2\sqrt{5}}\arctan{\frac{x\sqrt{5}}{2\sqrt{1-x^2}}}+C$$ But, since $-1 < x < 1$, how does it affect the integral?