Potentially more general statement about linearity of integrals

[DanielSank]

Here it is stated that we can break up sums inside of integrals.

Note that this is generally true:

\int f(x) + g(x) = \int f(x) + \int g(x)

One way to think about this is that the act of integration is linear. Think of the indefinite integral as a function that maps {functions of a real variable} to {functions of a real variable}. For example, the indefinite integral maps x^2 to (1/3)x^3. So, as a function, integration is linear because the integral of a sum of functions is equal to the sum of the integral of those functions.