Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 321: 67

$b$ is a solution to the given problem.

We are given that $\dfrac{dy}{dx}=\sec x$ $\dfrac{d}{dx}[\int_{0}^{x} \sec t dt+4]=\sec x+0=\sec x$ This implies that $y(0)=\int_{0}^{0} \sec t dt+4 =0+4=4$ Thus, $b$ is a solution to the given problem.