Set your WiFi AP's IP address to automatic, disable its DHCP server and set it to bridge mode.
That way, your other router will hand out IP addresses to the WiFi clients in the same range as the wired clients.
If your WiFi AP does not support bridge mode, then you'll have to pick a different IP range for your WiFi AP's clients, and make sure that you set your WiFi AP's default gateway (and primary DNS) to your wired router's LAN IP address. If your WiFi AP can get an IP address automatically, then everything should just work out of the box.