Answer
True
Work Step by Step
$$\int_a^b[f(x) + g(x)]dx = \lim\limits_{n \to \infty}\sum_{i=1}^n[f(x_i) + g(x_i)]\Delta x$$
$$= \lim\limits_{n \to \infty}[\sum_{i=1}^nf(x_i)\Delta x + \sum_{i=1}^ng(x_i)\Delta x]$$
$$= \lim\limits_{n \to \infty}[\sum_{i=1}^nf(x_i)\Delta x ]+ \lim\limits_{n \to \infty}[\sum_{i=1}^ng(x_i)\Delta x]$$
$$= \int_a^b f(x)dx + \int_a^b g(x)dx$$
