Answer
$$F(t) = 3\sin t+4\cos t+C $$
Work Step by Step
Given $$f(t) = 3\cos t-4\sin t$$
Then by using table 2 if $f(x)=\sin x\ \to\ \ F(x) =-\cos +C$ and if
$f(x)=\cos x\ \to\ \ F(x) =\sin x +C$
Hence
\begin{align*}
F(t) &= 3\sin t+4\cos t+C
\end{align*}
To check
\begin{align*}
F'(t) &= 3\cos t-4\sin t\\
&=f(t)
\end{align*}
