Broadcasts will not cross a layer-3 boundary (router). If the switches are connected to the router in separate subnets, the broadcast will be limited to a single switch. If the switches are bridged at layer-2, the broadcast will be propagated to any switch in the bridge group.
Basically, if traffic from one switch to the other must be routed (different subnets), broadcasts will be limited to a single switch.
If the switches only connect to the router at layer-3, broadcasts will be limited to a single switch. If the switches are connected to the router in a bridge group, the router acts like another layer-2 device for any traffic between the switches, and will pass layer-2 traffic (like broadcasts) between the switches. If the switches are connected together, layer-2 traffic will pass from one switch to another switch.
You need to define the layer-2/layer-3 boundaries in order to properly answer this question. Once you do that, you can tell where a broadcast will travel since it will not cross such a boundary.