Host A wants to send something to Host B who is in a different network. Between them is Router 1. Host A sends an ARP broadcast but Router 1 is not answering it. Why is that so?
The router will not do this by default, unless you enable Proxy ARP on that router's interface(s), but best practices dictate Proxy ARP should be disabled wherever possible.
However, host A should know by analyzing its own subnet mask (binary AND against its own subnet mask and Host B's address) that Host B is on a different network, and instead send the traffic to its default gateway (if one is configured), and if necessary, Host A will ARP for its default gateway's MAC address, which the router should respond to when appropriate.