Shrinking towards $1$ with weight $\tfrac12$ dominates $X$ when $\operatorname{Var} X=\mu^2+1$

Let X be a single observation with unknown mean $E(X)=\mu\in(-\infty,\infty)$ and variance $\operatorname{Var}(X)=\mu^2+1$. Consider the problem of estimating $\mu$ based on X under the squared error loss $L(\mu,a)=(a-\mu)^2$. Let $T_1=X$, $T_2=X/2+1/2$. Which of the following statements is true?