First ascertain the current version of mysql installed, the system architecture and OS release

rpm -qa|grep -i mysql
MySQL-devel-5.0.81-0.glibc23
MySQL-shared-5.0.81-0.glibc23
MySQL-client-5.0.81-0.glibc23
MySQL-server-5.0.81-0.glibc23
MySQL-bench-5.0.81-0.glibc23
arch
x86_64
cat /etc/redhat-release
CentOS release 5.3 (Final)

Next step is to download the latest MySQL 5.1 community release matching the OS and architecture from
http://dev.mysql.com/downloads/mysql/5.1.html#downloads

wget http://dev.mysql.com/get/Downloads/MySQL-5.1/MySQL-server-community-5.1.35-0.rhel5.x86_64.rpm/from/http://mirror.csclub.uwaterloo.ca/mysql/
wget http://dev.mysql.com/get/Downloads/MySQL-5.1/MySQL-client-community-5.1.35-0.rhel5.x86_64.rpm/from/http://mirror.csclub.uwaterloo.ca/mysql/
wget http://dev.mysql.com/get/Downloads/MySQL-5.1/MySQL-shared-community-5.1.35-0.rhel5.x86_64.rpm/from/http://mirror.csclub.uwaterloo.ca/mysql/
wget http://dev.mysql.com/get/Downloads/MySQL-5.1/MySQL-devel-community-5.1.35-0.rhel5.x86_64.rpm/from/http://mirror.csclub.uwaterloo.ca/mysql/

The download folder should look something like

ls
./ MySQL-client-community-5.1.35-0.rhel5.x86_64.rpm MySQL-server-community-5.1.35-0.rhel5.x86_64.rpm
../ [...]