Answer
$$H(\theta) =-2\cos \theta -\tan\theta+C $$
Work Step by Step
Given $$h(\theta) = 2\sin \theta -\sec^2\theta$$
Then by using table 2 if $f(x)=\sin x\ \to\ \ F(x) =-\cos +C$ and if
$f(x)=\sec^2x\ \to\ \ F(x) =\tan x +C$
Hence
\begin{align*}
H(\theta) &=-2\cos \theta -\tan\theta+C
\end{align*}
To check
\begin{align*}
H'(\theta) &= 2\sin \theta -\sec^2\theta\\
&=h(\theta)
\end{align*}
