How can JavaScript be integrated with PHP to achieve the desired functionality of hiding and showing boxes on a webpage?

To achieve the functionality of hiding and showing boxes on a webpage using JavaScript and PHP, you can use PHP to dynamically generate the HTML elements with unique IDs and then use JavaScript to toggle their visibility based on user interaction.

```php
<?php
for ($i = 1; $i <= 3; $i++) {
    echo "<div id='box$i' style='display: none;'>Box $i</div>";
}
?>
```

This PHP code snippet will generate three div elements with unique IDs (box1, box2, box3) and initially hide them using inline CSS.