Answer
$$f(x)=1+\cos x$$
Work Step by Step
Given: Slope$=-\sin x$ and passes through $(0,2)$
The curve is given by
\begin{align*}
f(x)&=\int (-\sin x)dx\\
&=\cos x+c
\end{align*}
Since the curve passes through $(0,2)$, then $c=1$ and
$$f(x)=1+\cos x$$
