I have to calculate this integral $\displaystyle \int_{ \beta }^{}$ $\displaystyle |z|dz$

when $\displaystyle \beta = [-i,i]$

so

$\displaystyle \gamma (t)= -i + ti$, $\displaystyle t \in [0,2]$

$\displaystyle \int_{0}^{2} |-i+ti|idt = i \int_{0}^{2} \sqrt{(t-1)^2} dt = i \int_{0}^{2} |t-1| dt = i (\int_{1}^{2} (t-1) dt - \int_{0}^{1} (t-1) dt ) = ... $

correct?