计算 $\boldsymbol{I}=\int_{\frac{1}{4}}^{\frac{1}{2}} \mathrm{~d} y \int_{\frac{1}{2}}^{\sqrt{y}} e^{\frac{y}{x}} \mathrm{~d} x+\int_{\frac{1}{2}}^1 \mathrm{~d} y \int_y^{\sqrt{y}} e^{\frac{y}{x}} \mathrm{~d} x$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$