replacing cast iron pipe?

Hello,

This morning my wife was washing dishes, and I noticed soapy water bubbling up outside in the yard. I dug up the pipe and it appears to be cast-iron and completely rusted through on the bottom of just this section. The pipes running above it look ok, but the plastic sheath is cracked and breaking off.

Will I be able to just cut out this section and replace it with a pvc pipe? I was told it might be hard to find a replacement because it's older pipe (house was built in the 60's.) I ran the water in the bathrooms and nothing leaked, so it looks like this line is just for the kitchen.

I don't have much experience with plumbing outside of replacing a few sinks and garbage disposals.

I just did this at my brother inlaws house from where it enters
the floor to 10' outside the house it all looked like your pics
it's not hard just labor intesnsivechange as much as you can
those are rubber push gaskets the pipe will come out with a sledge
hammer find good pipe on both ends cut with a sawzall(cast iron
blades) and reconnect with 4band couplings

put a clean out outside so if there is a stoppage you can
snake the mess will be outside rather than in the house

Thanks for the reply, that pipe ran to the cleanout, and the entire thing was rusted out. Had to cut it out, and cut ~6 inches of pipe further under the house out. The rest under the slab was, thankfully, in good shape.

Ran a 23-foot pvc out to the main drain line, and tied into it. It's still a bit wonky, the way the cast iron coming from under the house was, it wasn't a perfect fit. Besides the rubber sleeve, it's taped up and sprayed with flex-seal. It's not leaking, I just don't know how long it will last.