Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 5

W is a vector subspace of V.

Since the sum of continuous functions is continuous and the multiplication of a continuous function by a scalar is continuous, then $W$ the set of all functions that are continuous on $[-1,1]$ is a vector subspace of the set of all functions that are integrable on $[-1,1]$.