You can use the Business Hours object in the salesforce to attain this functionality.

Salesforce Documentation Link for Business Hours

Here is one example for using it -

    Date txnDate = System.today();
    Date systemDate = txnDate.addDays(10);

    Integer holidaysCount = 0;
    BusinessHours bh;
    List<BusinessHours> temp = [SELECT ID, Name, IsDefault, IsActive From BusinessHours 
                                    WHERE IsDefault = true 
                                    OR Name = 'BANK'];
    for (BusinessHours b : temp) {
        if (b.IsDefault) {
            bh = b;
        }
    }
    while (txnDate != systemDate) {
        Datetime now = Datetime.newInstance(txnDate.year(), txnDate.month(), txnDate.day(), 0, 0, 0);        
        Boolean isHoliday = !BusinessHours.isWithin(bh.Id, now);
        System.debug('The value of isHoliday is : '+isHoliday);
        if (isHoliday) {
            holidaysCount++;
        }
        txnDate = txnDate.addDays(1);
    }
    System.debug('The holidays are : '+holidaysCount);

You can use the Business Hours object in the salesforce to attain this functionality.

Salesforce Documentation Link for Business Hours

Here is one example for using it -

    Date txnDate = System.today();
    Date systemDate = txnDate.addDays(10);

    Integer holidaysCount = 0;
    BusinessHours bh;
    List<BusinessHours> temp = [SELECT ID, Name, IsDefault, IsActive From BusinessHours 
                                    WHERE IsDefault = true 
                                    OR Name = 'BANK'];
    for (BusinessHours b : temp) {
        if (b.IsDefault) {
            bh = b;
        }
    }
    while (txnDate != systemDate) {
        Datetime now = Datetime.newInstance(txnDate.year(), txnDate.month(), txnDate.day(), 0, 0, 0);        
        Boolean isHoliday = !BusinessHours.isWithin(bh.Id, now);
        System.debug('The value of isHoliday is : '+isHoliday);
        if (isHoliday) {
            holidaysCount++;
        }
        txnDate = txnDate.addDays(1);
    }
    System.debug('The holidays are : '+holidaysCount);