Mathematics

Problem

Let a function

f: \left[\frac{\pi}{2}, \pi\right] \rightarrow R

be defined as

f(x) = \int_{\frac{\pi}{2}}^x (\cos t - 2 \sin t) \,dt.

The greatest value of

f(x)

is (a) 0 (b)

\frac{\pi}{4}

(c)

\frac{\pi}{3}

(d)

\frac{\pi}{2}