Chapter 7.1, Problem 38P

Given that $0<a<b$. Let $f\left(t\right)=1$ if $a\underset{\_}{\underset{\_}{<}}t<b,f\left(t\right)=0$ if either $t<a$ or $t\underset{\_}{\underset{\_}{>}}b$. First, sketch the graph of the function f, making clear its values at t = a and t = b. Then express f in terms of unit step functions to show that ${L}\left\{f\left(t\right)\right\}=s^{-1}\left(e^{-as}-e^{-bs}\right)$ .