Change of Variable for Time Invariance Check

Question

I've been studying for a signals and systems class coming this fall and can't figure out how the following change of variable is being applied according to standard definition: $$T[x(t-\sigma)] = \int_t^0{\tau^2x(\tau-\sigma)d\tau} + x(t-\sigma) $$ $$= \int_{t-\sigma}^{-\sigma}{(\tau' + \sigma)^2x(\tau')d\tau'} + x(t-\sigma)$$ Where the change of variable $\tau-\sigma \rightarrow \tau'$ is applied. $$$$