How we can add two date intervals in PHP

This function allows you to combine any number of DateIntervals

/**
 * Combine a number of DateIntervals into 1 
 * @param DateInterval $...
 * @return DateInterval
 */
function addDateIntervals()
{
    $reference = new DateTimeImmutable;
    $endTime = clone $reference;

    foreach (func_get_args() as $dateInterval) {
        $endTime = $endTime->add($dateInterval);
    }

    return $reference->diff($endTime);
}

PHP has no operator overloading* so + with objects makes PHP trying it to convert them to string first, but DateInterval does not support that:

interval 1: 03:05
interval 2: 05:00
Total interval : 08:05

Instead you need to create a new DateTime object, then use the add function to add the intervals and finally display the difference to the reference point:

$e = new DateTime('00:00');
$f = clone $e;
$e->add($interval1);
$e->add($interval2);
echo "Total interval : ", $f->diff($e)->format("%H:%I"), "\n";

Full Example/(Demo):

$a = new DateTime('14:25');
$b = new DateTime('17:30');
$interval1 = $a->diff($b);
echo "interval 1: ", $interval1->format("%H:%I"), "\n";

$c = new DateTime('08:00');
$d = new DateTime('13:00');
$interval2 = $c->diff($d);
echo "interval 2: ", $interval2->format("%H:%I"), "\n";

$e = new DateTime('00:00');
$f = clone $e;
$e->add($interval1);
$e->add($interval2);
echo "Total interval : ", $f->diff($e)->format("%H:%I"), "\n";

---

You might also want to consider looking how DateInterval stores its' values and then extend from it to do the calculation your own. The following example (Demo) is rough, it does not take into account the inverted thingy, it does not (re)set $days to false and I have not checked/tested the ISO specification of the period specifier on creation but I think it is enough to show the idea:

class MyDateInterval extends DateInterval
{
    /**
     * @return MyDateInterval
     */
    public static function fromDateInterval(DateInterval $from)
    {
        return new MyDateInterval($from->format('P%yY%dDT%hH%iM%sS'));
    }
                                  
    public function add(DateInterval $interval)
    {
        foreach (str_split('ymdhis') as $prop)
        {
            $this->$prop += $interval->$prop;
        }
    }
}

$a = new DateTime('14:25');
$b = new DateTime('17:30');
$interval1 = $a->diff($b);
echo "interval 1: ", $interval1->format("%H:%I"), "\n";

$c = new DateTime('08:00');
$d = new DateTime('13:00');
$interval2 = $c->diff($d);
echo "interval 2: ", $interval2->format("%H:%I"), "\n";
                                  
$e = MyDateInterval::fromDateInterval($interval1);
$e->add($interval2);
echo "Total interval: ", $e->format("%H:%I"), "\n";

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^* If you write a PHP extension, it actually is possible (at least sort-of).