Evaluate $\int_{C}(x+y) d s, C: x=2 t, y=-2 t+2$, for $-1 \leq t \leq 1$

Step 1 ：Given the line integral \(\int_{C}(x+y) d s\), where the curve C is parameterized by \(x=2 t\) and \(y=-2 t+2\) for \(-1 \leq t \leq 1\)

Step 2 ：Substitute the parameterizations of x and y into the integral to get \(\int_{C}(2t - 2t + 2) d s\)

Step 3 ：Simplify the integral to \(\int_{C}2 ds\)

Step 4 ：Calculate the integral of ds from -1 to 1 to get 4

Step 5 ：Thus, the value of the line integral over the curve C is \(\boxed{4}\)