difficulty working out equation $\int_{-a}^{a}2(\sqrt{a^2-x^2})dx $ =$\left.2[\frac{1}{2}\sqrt{a^2-x^2}+a^2\arcsin(\frac{x}{a})]\right|_{-a}^{a}$ I encountered the below formula in my text.
I know the author is using integration by substitution and double angle formula
but for some reason, every working on paper that i did is different from the answer below:  
$\int_{-a}^{a}2(\sqrt{a^2-x^2})dx $
=$\left.2[\frac{1}{2}(\sqrt{a^2-x^2}+a^2\arcsin(\frac{x}{a}))]\right|_{-a}^{a}$   
Can anyone help me to expand the above equation.
I can't wrap my head on how above answer is reproduced.
Thanks.  

let $x = a \sin(u)$
then use
$\sin^2(u) + \cos^2(u) = 1$
