A circle of radius 2 is centered at O. Square O A B C has side length 1 . Sides \overline{A B} and \overline{C B} are extended past B to meet the circle at D and E, respectively. What is the area of the shaded region in the figure, which is bounded by \overline{B D}, \overline{B E}, and the minor arc connecting D and E ?
Answer Choices
A. \dfrac{\pi}{3}+1-\sqrt{3}
B. \dfrac{\pi}{3}-1+\sqrt{3}
C. \pi(2-\sqrt{3})
D. \dfrac{\pi}{6}+\dfrac{\sqrt{3}-1}{2}
E. \dfrac{\pi}{3}-1+\sqrt{3}