Crazy Limits!!! 1

Calculus Level 5

Let

$\displaystyle I = \lim_{x \to 0}\left(\frac{1}{x^{5}} \int_0^{x} e^{-t^{2}}dt -\frac{1}{x^{4}} + \frac{1}{3x^{2}} \right)$

and

$\displaystyle K= \lim_{n \to \infty}\left(\frac{[1^{2}\sqrt{7}] + [2^{2}\sqrt{7}]+ \ldots + [n^{2}\sqrt{7}]}{n^{3}} \right) .$

Then find

$\displaystyle \pi^{2} \times I + \frac{9K^{2}}{4}.$

Details and Assumptions