Chapter 4 - Integration - 4.6 The Fundamental Theorem Of Calculus - Exercises Set 4.6 - Page 320: 28

True.

True, by the Mean Value Theorem, we know that there is a point $x^{*}$ in $[a, b]$ such that \[ \int_{a}^{b} f(x) d x=0=(-a+b) f\left(x^{*}\right) \] Since $b \neq a,$ we know that $f\left(x^{*}\right)=0$, so the equation $f(x)=0$ has at least one solution in the interval $[a, b]$.