设 $f(x)$ 在 $(-\infty,+\infty)$ 内为连续的奇函数, $a$ 为常数, 则必为偶函数的是
$\text{A.}$ $\int_0^x \mathrm{~d} u \int_a^u t f(t) \mathrm{d} t$
$\text{B.}$ $\int_a^x \mathrm{~d} u \int_0^u f(t) \mathrm{d} t$
$\text{C.}$ $\int_0^x \mathrm{~d} u \int_a^u f(t) \mathrm{d} t$
$\text{D.}$ $\int_a^x \mathrm{~d} u \int_0^u t f(t) \mathrm{d} t$