设 $0 < a < 1, I_1=\int_0^1 \frac{\mathrm{e}^{a x}-1}{\mathrm{e}^x-1} \mathrm{~d} x, I_2=\int_0^1 \frac{\sqrt{a x}+1}{\sqrt{x}+1} \mathrm{~d} x$, 则
$\text{A.}$ $I_1 < a < I_2$.
$\text{B.}$ $I_2 < a < I_1$.
$\text{C.}$ $a < I_1 < I_2$.
$\text{D.}$ $I_1 < I_2 < a$.