Help identifiyng engine hose

[bmw328alpine]

I have been having a misfiring problem on idle and my engine power is sometime erratic so replaced the plugs and coils after reading the ecu fault codes. This did not fix the problem so checked the hoses and found 2 had cracked or perished! 1 is the intake filter elbow attached to the air flow sensor and the 2 I have no idea what its called! can some 1 tell me the hose name? and tell me what problem this might cause? https://1drv.ms/f/s!AvKwA7ZfmQIpgQpK0e_ocq11ILeV
You can see in the close up the hose has split!
My car is a 328ci

[TonyAngel]

Split hoses that are meant to carry air or ensure the lack of it cause vacuum leaks and throw the computers out of whack. I'd suggest getting on realoem.com with the last 7 digits of your VIN and look at the diagrams.

[dhurley34]

The hose's name is James.

[bmw328alpine]

I Went to my local BMW dealership with a photo as was told its the crank case ventilation hoses! £30 for the hose but told to replace all at a cost of £250. Did a search on ebay £58 for Febi/bilstein brand. Hopefully this fixes the misfire