AHSME 1975 Problem 27

If $p, q$ and $r$ are distinct roots of $x^3-x^2+x-2=0$, then $p^3+q^3+r^3$ equals $\textbf{(A)}\ -1 \textbf{(B)}\ 1 \textbf{(C)}\ 3 \textbf{(D)}\ 5 \textbf{(E)}\ \text{none of these}$