It seems there is no text in the provided image, only a mathematical expression. Here is the expression in LaTeX format:

```
\int_{0}^{1} \frac{x^4(1-x)^4}{1+x^2} \, dx = \frac{22}{7} - \pi
```

If you need the expression translated into a textual description, please let me know!
We can assume that the difference $d$ of the progression is positive and not a multiple of 10. Let $d$ be a $k$-digit number.

a) The numbers from A890...0 to A9...9 ($k+2$ nines) all contain nines. There are more than $d$ such numbers. The distance between two consecutive groups of such numbers is $89 \cdot 10^{k} \leq 89 d$. Therefore, the number of terms in the sequence is no more than 90.
b) When transitioning from any term of the sequence to the next, i.e., by adding the number $d$, the $(k+1)$-th digit either remains unchanged or increases by 1 (the digit 9 is forbidden, so the case of changing from 9 to 0 is excluded). If there are no transitions with a change in the $(k+1)$-th digit in the progression, then the number of terms in the progression is no more than 9. Suppose such transitions exist. Since the digit 9 is forbidden, there are no more than 8 such transitions. Between two such transitions, as well as before the first and after the last, there are groups (which may be empty) of transitions without changing the $(k+1)$-th digit. There are a total of 9 such groups.

Consider the term of the progression that stands before a transition that changes the $(k+1)$-th digit. Since it does not contain 9, its $k$-digit "tail" (remainder when divided by $10^{k}$) is no more than $\underbrace{88 \ldots 88}_{k \text{ times}}$. But when adding $d$, a carry must occur. Therefore, $d > \underbrace{11 \ldots 11}_{k \text{ times}}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_d9b26d382f9c77aca61cg-30.jpg?height=60&width=1976&top_left_y=507&top_left_x=41)
The $k$-digit tails themselves form an arithmetic progression with the same difference: $b_{m}, b_{m+1}, \ldots, b_{m+L}$. But $b_{m} \geq 0, b_{m+L}=b_{m}+d L \leq \underbrace{88 \ldots 88}_{k \text{ times}}$, hence $L \leq 7$.

Thus, the total number of terms in the progression is no more than $7 \cdot 9 + 8 + 1 = 72$.

c) An example of the required progression is given by the progression with the first term 1 and difference 125. Its 72nd term is 8876.