Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.6 Logarithmic And Other Functions Defined By Integrals - Exercises Set 6.6 - Page 460: 21

$\bf{False}$

We can see that the given function def$f(t)=\dfrac{1}{t}$ is not defined when $t=0$. This implies that the function is not continuous on the interval $[-1,e]$ and so, we cannot apply the Fundamental Theorem of calculus for the given integral. Hence, the given statement is $\bf{False}$.