There are many integral theorems dealing with the fundamental theorem of calculus.

The line integral in a vector field is usually an integral of the dot product $\displaystyle \vec F\cdot d\vec r$. The version of the fundamental theorem of calculus which applies to line integrals in a vector field states that if $\displaystyle \vec F(p)$ is the gradient of some scalar field $\displaystyle G(p)$ then $\displaystyle \int_{p_1}^{p_2}\vec F\cdot d\vec r = G(p_2)-G(p_1)$. Try to set $\displaystyle \vec F$ equal to the gradient of some unknown scalar field $\displaystyle G$ and see if you can find $\displaystyle G$ and then apply the theorem. If you cannot find $\displaystyle G$ then you will need to evaluate the integral directly by using the given parametrization, and using that

$\displaystyle \int_{p_1}^{p_2}\vec F(\vec r)\cdot d\vec r = \int_{t_1}^{t_2}\vec F(\vec r(t))\cdot \vec r\ '(t) dt$

where $\displaystyle \vec r (t) \ \ (t_1 \leq t \leq t_2)$ is your parametrization.