if the integral is convergent?

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my question is as this

$$ (M_{33}+\textrm{m}_{33})x''(t) + \int\limits_{-\infty }^t x'(t)K_{33}(t - \tau)\,d\tau = {F_3}(t)\\ {K_{33}}(t) = \frac{2}{\pi }\int\limits_0^{+\infty } b_{33}(\omega)\cos(\omega t)\,d\omega \\ b_{33}(\omega ) = \frac{C_k}{\omega ^7},\quad C_k = 0.25\\ $$

in the essay it seems that the integral are all converged, so when $t=0$,what is the value of $K_{33}$ and when $t=+\inf$,what is the value of $K_{33}$