I want to find
$$\int_C (x^2 dx + y^2 dy + z^2 dz),$$
where $C$ is the curve consisting of line segments from $(0,1,0)$ to $(1,0,1)$ and then from $(1,0,1)$ to $(2,1,3)$.
I attach my working out in the below link that I have done - please take a look at it and tell me if I am wrong, or correct me.
[![enter image description here][2]][2]
Any response would be kindly appreciated.
-nomad609
$$C_1:\left\{\begin{matrix} x=t & \\ y=1-t &, \ t \in\left [ 0, 1 \right ] \\ z=t & \end{matrix}\right.\\ C_2:\left\{\begin{matrix} x=t+1 & \\ y=t &, \ t \in\left [ 0, 1 \right ] \\ z=2t+1 & \end{matrix}\right.\\ \mathrm{Then} \ \int_{C}{x^2dx+y^2dy+z^2dz}=\int_{C_1}{x^2dx+y^2dy+z^2dz}+\int_{C_2}{x^2dx+y^2dy+z^2dz}=\\ =\int_{0}^{1}\left ( t^2-\left ( 1-t \right )^2+t^2 \right )dt+\int_{0}^{1}{\left ( t+1 \right )^2+t^2+2\left ( 2t+1 \right )^2}dt=\frac{35}{3}$$