Use Geometry to Compute the Given Integral $\int _ { - \frac { \pi } { 6 } } ^ { \frac { \pi } { 6 } } 2 \sin x d x$

Use geometry to compute the given integral. $\int _ { - \frac { \pi } { 6 } } ^ { \frac { \pi } { 6 } } 2 \sin x d x$

A) $\int _ { - \frac { \pi } { 6 } } ^ { \frac { \pi } { 6 } } 2 \sin x d x = 6$
B) $\int _ { - \frac { \pi } { 6 } } ^ { \frac { \pi } { 6 } } 2 \sin x \mathrm {~d} x = - 4$
C) $\int _ { - \frac { \pi } { 6 } } ^ { \frac { \pi } { 6 } } 2 \sin x d x = 0$
D) $\int _ { - \frac { \pi } { 6 } } ^ { \frac { \pi } { 6 } } 2 \sin x d x = 8$
E) none of these

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