#### Answer

A vector-valued function, or a vector function, is a function whose domain is a set of real numbers and whose range $\bf{R}$ is a set of multidimensional vectors.Consider any vector function in form of $r(t)=f(t)i+g(t)j+h(t)k$
To differentiate the vector function, we will differentiate each component separately to get:
$r'(t)=f'(t)i+g'(t)j+h'(t)k$
To integrate the vector function, we will integrate each component separately to get:
$\int r(t)=\int f(t)i+\int g(t)j+\int h(t)k$