The coordinates of the midpoint of a line segment with endpoints $G(x_1, y_1)$ and $H(x_2, y_2)$ can be found by averaging the coordinates of the endpoints. The $x$-coordinate of the midpoint is $(x_1 + x_2)/2$ and the $y$-coordinate of the midpoint is $(y_1 + y_2)/2$. Plugging in $x_1 = -2$, $y_1 = 5$, $x_2 = 4$, and $y_2 = 1$, we find that the midpoint is $\left(\dfrac{-2+4}{2}, \dfrac{5+1}{2}\right) = \boxed{\textbf{(A) }(2, 6)}$.
