Statistical Inference — unbiasedness of two mean estimators

Assume a sample of continuous random variables $X_1, X_2, X_3, …, X_n$ such that $E(X_i) = \mu$, $\operatorname{Var}(X_i) = \sigma^2 > 0$; $i = 1, 2, 3, …, n$. Define $\hat\mu_{1,n} = X_n$ and $\hat\mu_{2,n} = \frac{1}{n+1}\sum_{i=1}^{n}X_i$. Consider the following statements: I. $\hat\mu_{1,n}$ is an unbiased estimator of $\mu$. II. $\hat\mu_{2,n}$ is an unbiased estimator of $\mu$. Which of the statements given above is/are correct?