Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - True-False Review - Page 694: d

False

Let us consider an example: $f(x)=g(x)=1$ and $f(x-3)=1=g(x)$ Now, $\int_0^1 f(t) \ dt =1$ and $\int_0^1 g(t) \ dt =1$ This implies that the equality is not correct because $1\ne 1-3$ Therefore, the given statement is $\bf{False}$.