That is definitely repairable on the surface but be prepared to have to replace at least twice as much as what looks rotted. Fortunately, that rot is forward of the engine cross member so I doubt you will have any structural issues. The inside can be extremely difficult to access, damn near impossible in alot of cases. I did a ton of repair work between the firewall and the cross member and I actually ended up cutting out the bottom of the frame in a long segment to make sure I got most of the rust. After welding in fresh coated steal, I drilled a hole open in the frame and sprayed in rust reformer, let that set up for a few days and then hit it with internal frame coating.
Opening up the bottom of the frame all the way back to the firewall will give you access to the inside and let you determine what needs to be done. Fortunately, the vertical sides are what carry the load here, the bottom can usually be removed without compromising structural integrity as long as the motor is out of the car, which it appears to be.
I would just assume that you will have to replace the entire bottom of the frame from half a foot forward of that rot all the way back to the firewall. It slopes down towards the firewall so if any moisture was trapped in the frame it would accumulate towards that area most likely.