We can express the limit of the Riemann sum as a definite integral.
$$\lim_{n\to\infty} \sum_{k=1}^{n} c_k^2 \Delta x = \int_{a}^{b} f(x) dx$$
In this case, $f(x) = x^2$ and the interval is $[0,2]$. Therefore, the definite integral is:
$$\int_{0}^{2} x^2 dx$$
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