Evaluate the following integrals as limit of sum: `int_0^2 e^x dx`

Explanation

To evaluate the integral \(\int_0^2 e^x \, dx\) using the limit of sums, we will follow these steps:

### Step 1: Define the integral and the partition
We want to evaluate the integral from \(a = 0\) to \(b = 2\). We divide the interval \([0, 2]\) into \(n\) equal subintervals. The width of each subinterval is given by:
\[ h = \frac{b - a}{n} = \frac{2 - 0}{n} = \frac{2}{n} \]

...