Answer
$$\int_Cxydx+y^2dy+yzdz=\frac{110}{3}$$
Work Step by Step
$\int_Cxydx+y^2dy+yzdz=\int_0^1(2t+1)(4t)(2dt)+(4t)^2(4dt)+(4t)(3t-1)(3dt)$
$=\int_0^1(2t+1)(4t)(2dt)+(4t)^2(4dt)+(4t)(3t-1)(3dt)$
$=[\frac{116t^3}{3}-2t^2]_0^1$
$$\int_Cxydx+y^2dy+yzdz=\frac{110}{3}$$
