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It's easy to show that the system defined by $$y(t) = \int_{-\infty}^t x(\tau^2) d\tau$$ is Not Causal : it's because for for any value of $t$ the output $y(t)$ will always depend on future values of the input $x(t)$. Because while the dummy variable $\tau$ used in the integration ranges from $-\infty$ to $t$. The argument of the input function $x(t)$ ...