, 2004

The polynomial $f(x)$ satisfies the equation $f(x)-f(x-2)=(2x-1)^2$ for all $x$. If $p$ and $q$ are the coefficients of $x^2$ and $x$, respectively, in $f(x)$, then $p+q$ is equal to

(A) $0$ (B) $\dfrac{5}{6}$ (C) $\dfrac{4}{3}$ (D) $1$ (E) $\dfrac{2}{3}$