Answer $6\mathrm{.}3.$ PLEASE DO THIS BY PEN$/$PENCIL AND PAPER. Because last time I sent this question to an expert I got a solution that I couldn't read because it appeared like the following:

"The input$-$output relationship is:

$\backslash [$

y$($t$)=\backslash$int$\_\{$t$-$T$\}^$t $($t$-\backslash$tau$)^2$ x$(\backslash$tau$)\backslash ,$ d$\backslash$tau

$\backslash ]$

The impulse response $\backslash ($ h$($t$)\backslash )$ is the output when $\backslash ($ x$($t$)=\backslash$delta$($t$)\backslash ).$ Substitute $\backslash ($ x$($t$)=\backslash$delta$($t$)\backslash )$:

$\backslash ["$