Answer
See explanation.
Work Step by Step
This is a valid identity because the sum of the integeral is the sum of the integrals.
(a) $\int\left[f_{1}(x)+\ldots+f_{n}(x)\right] d x=\int f_{1}(x) d x+\ldots+\int f_{n}(x) d x$
This is a valid identity because the sum derivative is the sum of the derivatives.
(b) $\frac{d}{d x}\left[f_{1}(x)+\ldots+f_{n}(x)\right]=\frac{d}{d x} f_{1}(x)+\ldots+\frac{d}{d x} f_{n}(x)$
