Opposite of subtracting seconds from a java date, this example will show how to add seconds to a date using Calendar.add, java 8 date time api, joda DateTime.plusSeconds and apache common DateUtils.addSeconds. In the examples below, we will set a date that represents new years eve, December 31st, then add seconds to return a date representing new years day or January 1st.
Straight up Java
@Test
public void add_seconds_to_date_in_java () {
    Calendar newYearsEve = Calendar.getInstance();
    newYearsEve.set(2012, 11, 31, 23, 59, 0);
    Calendar newYearsDay = Calendar.getInstance();
    newYearsDay.setTimeInMillis(newYearsEve.getTimeInMillis());
    newYearsDay.add(Calendar.SECOND, 60);
    SimpleDateFormat dateFormatter = new SimpleDateFormat("MM/dd/yyyy HH:mm:ss z");
    logger.info(dateFormatter.format(newYearsEve.getTime()));
    logger.info(dateFormatter.format(newYearsDay.getTime()));
    assertTrue(newYearsDay.after(newYearsEve));
}Output
12/31/2012 23:59:00 CST
01/01/2013 00:00:00 CSTJava 8 Date and Time API
Java 8 LocalDateTime.plusSeconds will return a copy of the LocalDateTime with the specified number of seconds added.
@Test
public void add_seconds_to_date_in_java8() {
    LocalDateTime newYearsEve = LocalDateTime.of(2012, Month.DECEMBER, 31,
            23, 59);
    LocalDateTime newYearsDay = newYearsEve.plusSeconds(60);
    java.time.format.DateTimeFormatter formatter = java.time.format.DateTimeFormatter
            .ofPattern("MM/dd/yyyy HH:mm:ss S");
    logger.info(newYearsEve.format(formatter));
    logger.info(newYearsDay.format(formatter));
    assertTrue(newYearsDay.isAfter(newYearsEve));
}Output
12/31/2012 23:59:00 0
01/01/2013 00:00:00 0Joda Time
Joda DateTime.plusSeconds will return a copy the DateTime plus the specified number of seconds.
@Test
public void add_seconds_to_date_in_java_with_joda () {
    DateTime newYearsEve = new DateTime(2012, 12, 31, 23, 59, 0, 0);
    DateTime newYearsDay = newYearsEve.plusSeconds(60);
    DateTimeFormatter fmt = DateTimeFormat.forPattern("MM/dd/yyyy HH:mm:ss z");
    logger.info(newYearsEve.toString(fmt));
    logger.info(newYearsDay.toString(fmt));
    assertTrue(newYearsDay.isAfter(newYearsEve));
}Output
12/31/2012 23:59:00 CST
01/01/2013 00:00:00 CSTApache Commons
Apache commons DateUtils.addSeconds will adds a number of seconds to the date returning a new object.
@Test
public void add_seconds_to_date_in_java_with_apachecommons () {
    Calendar newYearsEve = Calendar.getInstance();
    newYearsEve.set(2012, 11, 31, 23, 59, 0);
    Date newYearsDay = DateUtils.addSeconds(newYearsEve.getTime(), 60);
    SimpleDateFormat dateFormatter = new SimpleDateFormat("MM/dd/yyyy HH:mm:ss z");
    logger.info(dateFormatter.format(newYearsEve.getTime()));
    logger.info(dateFormatter.format(newYearsDay));
    assertTrue(newYearsDay.after(newYearsEve.getTime()));
}Output
12/31/2012 23:59:00 CST
01/01/2013 00:00:00 CST