Chapter 5: Integrals - Section 5.4 - The Fundamental Theorem of Calculus - Exercises 5.4 - Page 287: 57

$b$ is a solution to the given problem.

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