Which statement correctly matches the mathematical operation to the quantity being sought?

Use an indefinite integral for both recovering $\overrightarrow{v}\left(t_{}\right)$ and finding $\Delta v$

Use an indefinite integral to recover $\overrightarrow{v}\left(t_{}\right)$ from $\overrightarrow{a}\left(t_{}\right)$, and a definite integral to find $\Delta v$ over a time interval

Use derivatives for both recovering $\overrightarrow{v}\left(t_{}\right)$ from $\overrightarrow{a}\left(t_{}\right)$ and finding $\Delta v$

Use a definite integral to recover $\overrightarrow{v}\left(t_{}\right)$ from $\overrightarrow{a}\left(t_{}\right)$, and an indefinite integral to find $\Delta v$ over a time interval