Chapter 5: Integrals - Section 5.4 - The Fundamental Theorem of Calculus - Exercises 5.4 - Page 287: 58

$a$ is a solution to the given problem.

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