Evaluate the line integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$grad$*dr$ for the following function $$ and oriented curve $C($a$)$ using a parametric description of $C$ and evaluating the integral directly, and $($b$)$ using the Fundamenta for line integrals.

$(x,y,z)=\frac{x^2+y^2+z^2}{2}$

$C$:$r(t)=($:$cost,sint,\frac{t}{}$:$),$ for $\frac{}{6}t\frac{5}{3}$

$($a$)$ Set up the integral used to evaluate the line integral using a parametric description of C $.$ Use increasing limits of integration.

dt $($Type exact answers.$)$

$($b$)$ Select the correct choice below and fill in the answer box$($es$)$ to complete your choice.

$($Type exact answers.$)$

A$.$ If $A$ is the first point on the curve, $,,$ and $B$ is the last point on the curve, $,),$ then the value of the line integral is $(A)-(B).$

B$.$ If $A$ is the first point on the curve, $,,,,$ and $B$ is the last point on the curve, $($

$),$ then the value of the line integral is $(A).$

C$.$ If A is the first point on the curve, $),$ then the value of the line integral is $(B)-(A).$

D$.$ If $B$ is the last point on the curve, $,$

$),$ then the value of the line integral is $(B).$

Using either method, ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$grad$*dr=$

$($Type an exact answer.$)$