Transforming Integration Solid angle under $\hat{x}^i\rightarrow-\hat{x}^i$

Question

Assume I have the following integral over the solid angle $$\int d\Omega_x=\int_{0}^{2\pi} d\phi_x\int_0^{\pi}\sin\theta_x d\theta_x$$ where $(\theta,\phi)$ are the spherical coordinates of a unit vector $$\hat{x}=\frac{1}{\sqrt{x^2+y^2+z^2}}(x,y,z)$$ Now I wish to perform the transformation $\hat{x}\rightarrow\hat{u}=-\hat{x}$. How will my integral over the solid angle change? I.e. what will $$\int d\Omega_u=\int_{0}^{2\pi} d\phi_u\int_0^{\pi}\sin\theta_u d\theta_u$$ be in terms of $\int d\Omega_x$ be?