Chapter 5.1, Problem 79E

Show that the indefinite integral of the sum of two functions is the sum of the indefinite integrals.

[Hint: Assume that ${\displaystyle \int f\left(x\right)}dx=F\left(x\right)+C_1$ and ${\displaystyle \int g\left(x\right)}dx=G\left(x\right)+C_2.$ Using differentiation, show that $F\left(x\right)+C_1+G\left(x\right)+C_2$ is the indefinite integral of the function s(x) = f(x) + g(x).]