当 $0 < x \leqslant \frac{\pi}{4}$ 时,下列不等式成立的是
$\text{A.}$ $\int_0^x \mathrm{e}^t \cos t \mathrm{~d} t>x, \int_0^x \mathrm{e}^t(1-\sin t) \mathrm{d} t < x$.
$\text{B.}$ $\int_0^x \mathrm{e}^t \cos t \mathrm{~d} t < x, \int_0^x \mathrm{e}^t(1-\sin t) \mathrm{d} t>x$.
$\text{C.}$ $\int_0^x \mathrm{e}^t \cos t \mathrm{~d} t>x, \int_0^x \mathrm{e}^t(1-\sin t) \mathrm{d} t>x$.
$\text{D.}$ $\int_0^x \mathrm{e}^t \cos t \mathrm{~d} t < x, \int_0^x \mathrm{e}^t(1-\sin t) \mathrm{d} t < x$.