Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 246: 66

$$1$$

Since $$ \int_{1}^{b} f(x) d x=1-b^{-1} \text { for all } b>0$$ then \begin{aligned} \int_{1 / 2}^{1} f(x) d x &=-\int_{1 }^{1/2} f(x) d x \\ &=-\left(1-(1 / 2)^{-1}\right) \\ &=-\left(1-\frac{1}{1 / 2}\right) \\ &=-(1-2) \\ &=1 \end{aligned}