What is this antiderivative? Does the limited domain of sec(x) affect my answer?

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Here are the equations I need to find the antiderivative of. Am I missing something?:

$$ h(\theta) = 2 \sin{\theta} - \sec^2{\theta}$$ Is it: $$ -2\cos{\theta} - tan{\theta}$$

and this one:

$$r({\theta}) = \sec{\theta} \cdot \tan{\theta} - 2e^{\theta}$$ Is $$ \sec({\theta}) - 2e^{\theta}$$ the antiderivate ?

These are my professors' comments which I cannot understand:

Note that $\sec(x)$ has a limited domain which you must take into account here – so your final answer is the same as you have, with the constant depending on $n$, i.e. $C_n$, and on the interval ($n\pi - \pi/2, n\pi + \pi/2$). ($-2$)