We are given a function $\int_{0}^{x} f(t)dt = x^2(1+x^2)$. To find $f(x)$, we differentiate both sides with respect to $x$. This follows from the Fundamental Theorem of Calculus.

Differentiate: $$\frac{d}{dx}\left(\int_{0}^{x} f(t) dt\right) = \frac{d}{dx}[x^2(1+x^2)].$$

By the Fundamental Theorem of Calculus, the left side becomes $f(x)$. Differentiate the right side with respect to $x$:

$$f(x) = \frac{d}{dx}[x^2(1+x^2)] = \frac{d}{dx}[x^2 + x^4].$$

Breaking it down: $$\frac{d}{dx}[x^2] = 2x$$ and $$\frac{d}{dx}[x^4] = 4x^3.$$

Therefore, $$f(x) = 2x + 4x^3.$$

Substitute $x=2$ to find $f(2)$: $$f(2) = 2(2) + 4(2)^3 = 4 + 4 \cdot 8 = 4 + 32 = 36.$$

Thus, $f(2) = 36$.

Upon comparison, the provided range was incorrectly stated as a minimum and maximum. Our computed solution $36$ does not fit "5,5". The correct range or comparison might have been incorrectly interpreted.