Google-sheets – Sum of cells within a given range of dates

This works, see F35 in your sheet:

SUMIF(E2:E33;">="&E35;B2:B33)-SUMIF(E2:E33;"<="&E36;B2:B33)

column E is done by calculating a value for the dates to be able to compare them (=VALUE(E1))

Note that separating the args for some reasons is done with ;

There are two ways for you to approach this. The first is via good old formula's. The second is via a Google Apps Script (GAS). The latter is done when the logic in the formula becomes too complex or too slow.

Solutions

(1) Formula
----------- 
=ARRAYFORMULA(IF(Dt!A2:A5=DATEVALUE("13/03/2013"),"Match","No Match"))

(2) Google Apps SCript
----------------------
function myCheck(range,year,month,day) {
  var output = [], myDate = new Date(year,month-1,day);

  for(var i in range) {
    var ckDate = new Date(range[i]);
    if(ckDate-myDate === 0) {
      output.push(["Match"]);
    } else {
      output.push(["No Match"]);
    }
  }
  return output;
}

Explained

1. The formula converts the string date to a date value and compares it to the range. If one of them is equal, then it will show/display the word "Match".
2. The code can be written without API calls. All dates are compared (substracted) and the outcome is pushed into an array and returned.

Example

I've created an example file for you: Looping Through Dates

Remarks to your Code

• Fiddling around with dates in GAS can be quite difficult. Use the Logger.log() method to capture intermediate results, so that you can evaluate them.
• When you declare something, use it; var sheet isn't used.
• If you want something to be declared, then do it; x isn't explicitly declared.
• I've rearranged your code a bit. See example file. Outcome is reversed to what you wanted....
• See script editor for your original code. I've added Logger.log() to see the intermediate results.