Let $f : \mathbb{R} \rightarrow (0,1)$ be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval $(0,1)$?
[A] $x^9 - f(x)$
[B] $x - \int_0^{\frac{\pi}{2} - x} f(t)\cos t\, dt$
[C] $e^x - \int_0^x f(t)\sin t\, dt$
[D] $f(x) + \int_0^{\frac{\pi}{2}} f(t)\sin t\, dt$