sifting property

Consider a continuous-time signal $$ x(t)=-t^2\{u(t+4)-u(t-4)\} $$ where $u(t)$ is the continuous-time unit step function. Let $\delta(t)$ be the continuous-time unit impulse funct...

The value of $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dirac delta function, is

The value of the integral $$\int_{-5}^{+6}e^{-2t}\delta\left(t-1\right)dt$$ is equal to ________.