Transform, Add, Integrate. Large?

Note that $\mathcal{L}^{-1} s^n = \delta^{(n)} \left(t\right)$ , and $\int _{-\infty }^{\infty }\:\delta ^{\left(n\right)}\left(t\right)dt = 0$ for nonzero $n$ , where $\delta (t)$ is the Dirac-Delta function. Thus the integrand simplifies to $3 \times 2\delta (t)$ . Since the infinite integral is equal to 1 for the Dirac-Delta function. Then the integral is equal to 6.