Chapter 5: Integrals - Section 5.4 - The Fundamental Theorem of Calculus - Exercises 5.4 - Page 287: 55

$d$ is a solution to the given problem.

Given: $\dfrac{dy}{dx}=\dfrac{1}{x}$ $\dfrac{d}{dx}[\int_0^{x} \dfrac{1}{t} dt ]-3=\dfrac{1}{x}$ $\implies y(\pi)=\int_{\pi}^{\pi} (\dfrac{1}{t}) dt -3$ $\implies y(\pi)= 0-3=-3$ Thus, the option $d$ is a solution to the given problem.