To get result set where Company field value lays between Edit1 and Edit2:
with Customer do
begin
EditRangeStart;
// Set start range based on text of Edit1 component
FieldByName('Company').AsString := Edit1.Text;
EditRangeEnd;
// Set end range based on value of Edit2 component
FieldByName('Company').AsString := Edit2.Text;
ApplyRange; // Apply the ranges
end;