NEVER use 2 'WHERE's in a single query!
$result1 = mysql_query("
SELECT *
FROM details
WHERE Rent>='$min_rent'
AND Rent<='$max_rent'
",$db);
If you can be certain that $min_rent will always be less than or equal to $max_rent, you can also use this construction:
$result1 = mysql_query("
SELECT *
FROM details
WHERE Rent
BETWEEN $min_rent'
AND '$max_rent'
",$db);
Ps. caPitaliZatioN MakEs a diFfErence -- rent or Rent, for example
PPS if Rent is a numeric field, your query will work faster if you DON'T put quotes around '$min_rent' and $max_rent.