Answer
$\frac{3}{\ln2}$
Work Step by Step
$A$ = $\int_{{\,-1}}^{{\,1}}$$2^{(1-x)}$ $dx$
$A$ = $2\int_{{\,-1}}^{{\,1}}$$2^{-x}$ $dx$
$A$ = $-2(\frac{2^{-x}}{\ln2})$ $|_{{\,-1}}^{{\,1}}$
$A$ = $\frac{-2}{\ln2}[({2^{-1}})-({2^{1}})]$
$A$ = $\frac{3}{\ln2}$