For a continuous function $f$ defined on the set of real numbers and the function $g(x) = 2x + 2$ defined as,
$$\begin{aligned}
& \int_{-1}^{1} f(g(x))\, dx = 18 \\
& \int_{2}^{4} g(f(x))\, dx = 18
\end{aligned}$$
are satisfied.
Accordingly, what is the value of the integral $\int_{0}^{2} f(x)\, dx$?
A) 20
B) 23
C) 26
D) 29
E) 32