Simpson's one-third rule is used to estimate the definite integral
$$
I=\int_{-1}^1 \sqrt{\left(1-x^2\right)} d x
$$
with an interval length of $0.5.$ Which one of the following is the $\text{CORRECT}$ estimate of $I$ obtained using this rule?
- $\frac{1}{3}-\frac{1}{\sqrt{3}}$
- $\frac{1}{3}+\frac{2}{\sqrt{3}}$
- $\frac{1}{3}+\frac{1}{\sqrt{3}}$
- $\frac{1}{3}-\frac{2}{\sqrt{3}}$