Chapter 5.4, Problem 65ES

By writing out the sums, determine whether the following are valid identities.

(a) ${\displaystyle \int \left[{\displaystyle \underset{i=1}{\overset{n}{\sum }}{f}_i\left(x\right)}\right]dx}={\displaystyle \underset{i=1}{\overset{n}{\sum }}\left[{\displaystyle \int f_i\left(x\right)dx}\right]}$

(b) $\frac{d}{dx}\left[{\displaystyle \underset{i=1}{\overset{n}{\sum }}{f}_i\left(x\right)}\right]={\displaystyle \underset{i=1}{\overset{n}{\sum }}\left[\frac{d}{dx}\left[f_i\left(x\right)\right]\right]}$