Calculus of Vector Valued Functions

I.

A vector‐valued function $\mathbf{r}(t)= \langle x(t), y(t) \rangle$ represents the position of an object in the plane.

II.

Its derivative is obtained by differentiating each component individually, i.e. $\mathbf{r}'(t)= \langle x'(t), y'(t) \rangle$.

III.

Similarly, the integral of a vector‐valued function is computed by taking the integral of each component separately.

Which of the statements above are true?