2002 AMC 12B Problem 25

Let f(x) = x^2 + 6x + 1, and let R denote the set of points (x,y) in the coordinate plane such that f(x) + f(y) \le 0 \qquad \text{and} \qquad f(x)-f(y) \le 0 The area of R is closest to

\mathrm{(A)}\ 21 \qquad\mathrm{(B)}\ 22 \qquad\mathrm{(C)}\ 23 \qquad\mathrm{(D)}\ 24 \qquad\mathrm{(E)}\ 25

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.