Answer
$c$ is a solution to the given problem.
Work Step by Step
As we are given that $\dfrac{dy}{dx}=\sec x$
$\dfrac{d}{dx}[\int_{-1}^{x} \sec t dt+4]=\sec x+0=\sec x$
This implies that
$y(-1)=\int_{-1}^{1} \sec t dt+4 =0+4=4$
Thus, $c$ is a solution to the given problem.