Determine whether the following equation is true or false.

${\displaystyle \underset{-1}{\overset{1}{}}}\frac{-1}{x^2}sin(\frac{1}{x})dx={\displaystyle \underset{-1}{\overset{1}{}}}sin(u)du$

Is the equation true or false?

A$.$ The equation is true by the substitution $u=\frac{1}{x}.$

B$.$ The equation is true by the substitution $u=\frac{1}{x^2}.$

C$.$ The equation is true by the substitution $u=sin(\frac{1}{x}).$

D$.$ The equation is false because $\frac{1}{x}$ is not continuous on $-1,1$