create table test1_3(id int primary key auto_increment,username varchar(10),start1 int,end1 int);

insert into test1_3(username,start1,end1) values('A',1,2);

insert into test1_3(username,start1,end1) values('A',3,4);

insert into test1_3(username,start1,end1) values('B',4,5);

insert into test1_3(username,start1,end1) values('A',6,7);

insert into test1_3(username,start1,end1) values('B',7,8);

insert into test1_3(username,start1,end1) values('A',8,9);

select * from test1_3;

select username,min(start1) start1,max(end1) end1 from (

select test1_3.* ,

                if(start1-1=@start1 ANd @username=username,@rn:=@rn,@rn:=@rn+1) as rn,

                @username:=username,

                @start1:=end1 as '@start'

 from test1_3 cross join (select @rn:=0,@start1:=0,@end1:=0,@username:='q') t

    order by username,start1

) t1 group by username,rn ;