Evaluate `int_(0)^(1)x^(2)dx` as the limit of a sum.

Explanation

To evaluate the integral \( \int_0^1 x^2 \, dx \) as the limit of a sum, we will follow these steps:

### Step 1: Set up the integral as a limit of a sum
The integral from \( a \) to \( b \) of \( f(x) \, dx \) can be expressed as:
\[ \int_a^b f(x) \, dx = \lim_{n \to \infty} \sum_{k=0}^{n-1} f\left(a + k \cdot h\right) \cdot h \]
where \( h = \frac{b-a}{n} \).
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