This question comes up a lot on Stack Overflow, so you'd be well advised to look through many of the similar ones to see there answers!
Excel stores almost all numbers in the file format as floating point values, which is why POI will give you back a double for a numeric cell as that's what was really there. If you want it to look like it does in Excel, you need to apply the formatting rules defined against the cell to the number. Thus, you want to do exactly the same thing as in my answer here. To quote:
What you want to do is use the DataFormatter class. You pass this a cell, and it does its best to return you a string containing what Excel would show you for that cell. If you pass it a string cell, you'll get the string back. If you pass it a numeric cell with formatting rules applied, it will format the number based on them and give you the string back.
For your case, I'd assume that the numeric cells have an integer formatting rule applied to them. If you ask DataFormatter to format those cells, it'll give you back a string with the integer string in it.
All you need to do is:
// Only need one of these
DataFormatter fmt = new DataFormatter();
// Once per cell
String valueAsSeenInExcel = fmt.formatCellValue(cell);