Chapter 5: Integrals - Section 5.4 - The Fundamental Theorem of Calculus - Exercises 5.4 - Page 287: 56

$c$ is a solution to the given problem.

Given: $\dfrac{dy}{dx}=\sec x$ $\implies \dfrac{d}{dx}[\int_{-1}^{x} \sec t dt]+4=\sec x+0=\sec x$ $\implies y(-1)=\int_{(-1)}^{1} (\sec t) dt+4 $ $\implies y(-1)=0+4=4$ Hence, the option $c$ is a solution to the given problem.