Optimize query execution based on two datetime columns

Thanks to everyone who took the time to respond. I got it fixed in a different way. Since the values can't overlap and mysql is efficient using one single index for ranges, what i did was find the first col1 and last col1 and use a select between. This turned out really fast because mysql now analyses only the lines in the range.

As for the aggregates which were causing problems I still had to go round them anyways because I had to execute it separately or otherwise MySQL optimizer was really inefficient. The way I did it was by selecting the results into a temporary memory table and then loop those results (cursor wasn't a choice because I already had a loop) and doing the 3 aggregate functions at once. This is was the final result (just the loop part):

myLoop: LOOP

IF (SELECT COUNT(*) FROM (SELECT
    @CarrId := carrier_id,
    @FistVTime := firstValidTIME,
    @LastVTime := lastValidTIME
FROM startStopReportTable
WHERE maxSpeed = -1) AS dummyTbl) < 1 THEN
    LEAVE myLoop;
END IF;

UPDATE startStopReportTable AS t0,
    (SELECT
        SUM(l0.distance) AS distance,
        AVG(l0.speed) AS avgspeed,
        MAX(l0.speed) AS maxspeed
        FROM
            pcoarg AS l0
        WHERE
            l0.carrier_id = @CarrId
        AND
            l0.lastValidTIME BETWEEN @FistVTime AND @LastVTime
    ) AS t1
SET
    t0.distance = t1.distance,
    t0.averageSpeed = t1.avgspeed,
    t0.maxSpeed = t1.maxspeed
WHERE t0.carrier_id = @CarrId AND t0.firstValidTIME = @FistVTime AND t0.lastValidTIME = @LastVTime;
END LOOP;

LastValidTIME is col1 startStopReportTable is temporary table

Profiling results:

96  0.00058100  UPDATE startStopReportTable AS t0,
      (SELECT
       SUM(l0.distance) AS distance,
       AVG(l0.speed) AS avgspeed,
       MAX(l0.speed) AS maxspeed
       FROM
        pcoarg AS l0
       WHERE
        l0.carrier_id = @CarrId
       AND
        l0.lastValidTI...
97  0.00045100  UPDATE startStopReportTable AS t0,
      (SELECT
       SUM(l0.distance) AS distance,
       AVG(l0.speed) AS avgspeed,
       MAX(l0.speed) AS maxspeed
       FROM
        pcoarg AS l0
       WHERE
        l0.carrier_id = @CarrId
       AND
        l0.lastValidTI...
98  0.00094900  UPDATE startStopReportTable AS t0,
      (SELECT
       SUM(l0.distance) AS distance,
       AVG(l0.speed) AS avgspeed,
       MAX(l0.speed) AS maxspeed
       FROM
        pcoarg AS l0
       WHERE
        l0.carrier_id = @CarrId
       AND
        l0.lastValidTI...

It's really a shame that the optimizer can't combine sub query aggregates in one query while it can combine them in one query.