AHSME 1952 Problem 28

In the table shown, the formula relating x and y is: $$\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5\\ \hline y & 3 & 7 & 13 & 21 & 31\\ \hline\end{array}$$ $\text{(A) } y = 4x - 1 \text{(B) } y = x^3 - x^2 + x + 2 \\ \text{(C) } y = x^2 + x + 1 \text{(D) } y = (x^2 + x + 1)(x - 1) \\ \text{(E) } \text{none of these}$