How can we prove the following asymptotic lower bound?

$$\lim_{n\to\infty}\int_0^{1} I_{2 t - t^2}\left(\frac{n - 1}{2}, \frac{1}{2}\right) dt=\Omega\left(\frac{1}{\sqrt{n}}\right)$$

How can we prove the following asymptotic lower bound for the regularized Beta function when $n\rightarrow\infty$?

$$\int_0^{1} I_{2 t - t^2}\left(\frac{n - 1}{2}, \frac{1}{2}\right) dt=\Omega\left(\frac{1}{\sqrt{n}}\right)$$