Chapter 4 - Integrals - 4.2 The Definite Integral - 4.2 Exercises - Page 318: 47

$\int_{-1}^{5}f(x)dx$

$$\begin{align*} &\int_{-2}^{2}f(x)dx+\int_{2}^{5}f(x)dx-\int_{-2}^{-1}f(x)dx\\ &=\left(\int_{-2}^{2}f(x)dx+\int_{2}^{5}f(x)dx\right)-\int_{-2}^{-1}f(x)dx\\ &=\int_{-2}^{5}f(x)dx-\int_{-2}^{-1}f(x)dx\\ &=\int_{-2}^{5}f(x)dx+\int_{-1}^{-2}f(x)dx\\ &=\int_{-1}^{-2}f(x)dx+\int_{-2}^{5}f(x)dx\\ &=\int_{-1}^{5}f(x)dx \end{align*}$$