This appears to be a problem involving the trapezoidal rule for numerical integration. The equation given is:

$\int \frac{dx}{1 + x^2} \quad \text{with} \quad h = \frac{1}{4}$

The solution uses the trapezoidal rule to evaluate the integral. Here's a breakdown of what is happening in the steps:

1. Given information: The trapezoidal rule formula for approximating integrals is: $I \approx \frac{h}{2} \left( f(x_0) + 2 \sum_{i=1}^{n-1} f(x_i) + f(x_n) \right)$ where $h$ is the step size, and $x_0, x_1, x_2, ..., x_n$ are the points at which the function is evaluated.

2. Step 1: The function is $f(x) = \frac{1}{1 + x^2}$, and the step size $h = \frac{1}{4}$. This means $x_0, x_1, x_2, \dots$ are calculated by adding $h$ incrementally starting from $x_0 = 0$.

The steps in the image are working through the evaluation of this formula using the given values of $h$. It uses successive values of $x$ (e.g., $x_0, x_1, x_2, x_3, x_4$) to calculate corresponding function values $y_0, y_1, y_2, y_3, y_4$, which are substituted into the trapezoidal rule formula.

Would you like me to walk you through the entire solution step-by-step or explain any particular part of the process in more detail?