Different types of line integrals Say for instance you were given that $\mathbf r = t^3 \vec i+t^2\vec j+t\vec k$ and $\mathbf A = sinx \vec i+cosy \vec j+xz \vec k$.
When calculating the line integral $$\oint\mathbf A \bullet d\mathbf r$$ do you do anything different to when calculating $$\int\mathbf A \bullet d\mathbf r$$?

In general there is no difference. However, if you know that $\mathbf{A}$ is a conservative field, then
$$\oint \mathbf{A} \cdot d\mathbf{r} = 0, \int_\gamma \mathbf{A} \cdot d\mathbf{r} = \mathbf{A}(\gamma(b)) - \mathbf{A}(\gamma(a))$$
where $\gamma(a),\gamma(b)$ are the starting and end points of $\gamma$, respectively.
