\(\bf \displaystyle \int -2t\cdot dt\implies -2\int t\cdot dt\implies -2\cdot \cfrac{t^2}{2}+C
\\\\\\
-t^2+C=f(x)\qquad
\begin{cases}
f(x)=y=1\\
t=0
\end{cases}\implies -0^2+C=1\implies C=1
\\\\\\
-t^2+1=f(x)\\\\
-----------------------------\\\\
-t^2+1=f(x)\qquad f(x)=\cfrac{1}{2}\implies -t^2+1=\cfrac{1}{2}
\\\\\\
1-\cfrac{1}{2}=t^2\implies \pm \sqrt{\cfrac{1}{2}}=t\implies \cfrac{1}{\pm \sqrt{2}}=t
\\\\\\
\pm \cfrac{\sqrt{2}}{2}=t\impliedby \textit{with a rationalized denominator}\)