I used to utilize ssh-agent as well as ssh-add to connect to a server via an intermediate server. There are two articles to explain the principle and the usage.
But this kind of directly forwarding is not secure for your private key REF, I recommend to use the ProxyCommand to release the aim.
Here is an example:
ProxyCommand ssh -q -W %h:%p hosta
This config gives a solution to connect hostb via hosta, which it will firstly connect hosta and use ProxyCommand to automatically connect hostb.