In the graph below, the function $f(x)$ is graphed with a bold, blue curve, and the function $g(x)$ with a light, red curve. Assume that the behavior of both functions as $x\to\infty$ is accurately suggested by the domain on which they are graphed in the figure.

Suppose $\int_a^{\infty} f(x)\, dx$ converges. What does this graph suggest about the convergence of $\int_{a}^{\infty}g(x)\,dx$?
A. $\int_{a}^{\infty}g(x)\,dx$ converges
B. $\int_{a}^{\infty}g(x)\,dx$ neither converges nor diverges
C. the graph does not provide enough information to suggest with any certainty whether $\int_{a}^{\infty}g(x)\,dx$ converges or diverges
D. $\int_{a}^{\infty}g(x)\,dx$ diverges