Evaluate the following definite integrals as limit of sums.`int_a^b xdx`

Explanation

To evaluate the definite integral \(\int_a^b x \, dx\) as a limit of sums, we will follow these steps:

### Step 1: Set up the limit of sums
The definite integral can be expressed as a limit of sums using the formula:
\[ \int_a^b f(x) \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i^*) \Delta x \]
where \(\Delta x = \frac{b - a}{n}\) and \(x_i^* = a + i \Delta x\).
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