Hi. I have finally solved my problem!!!
As I thought, the problem was in the expression. Now the code is:
import arcpy
from arcpy import env
env = "C:/Users/Desktop/an1"
inputfc = arcpy.GetParameterAsText(0)
outputfc = arcpy.GetParameterAsText(1)
dateFrom = arcpy.GetParameter(2)
dateTo = arcpy.GetParameter(3)
xyTolerance = arcpy.GetParameterAsText(4)
select = inputfc + "_sel"
where_clause = '"DATE" > date \'%s\' AND "DATE" < date \'%s\' ' % (dateFrom, dateTo)
arcpy.Select_analysis(inputfc, select, where_clause)
integrated = select + "_int"
arcpy.CopyFeatures_management(inputfc, integrated)
arcpy.Integrate_management(integrated, str(xyTolerance) + " Meters")
ce = arcpy.CollectEvents_stats(integrated, outputfc)
Hope it'' help someone in the future 