$(5)$ Compute the following line integrals:

a$)$ Let vec$(F)=$xvec$(i)+$yvec$(j)+$zvec$(k).$ Compute the line integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)dvec(R)$ over the curve $C$ parametrized

by $(x(t),y(t),z(t))=(sint,cost,t),$ with $0t2.$

b$)$ Let vec$(F)=x^2$vec$(i)+$xyvec$(j)+$vec$(k).$ Compute the line integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(R)$ over the curve $C$

parametrized by $(x(t),y(t),z(t))=(t,t^2,1),$ with $0t1.$