If the integral gutter is a nearly flat extension out over the roof edge also forming a soffit i d think about leaving the built in or integral gutter system in place removing any.
Gutters built into roof.
Built in gutter systems are actually built into the cornice structure and drain through internal or external leaders.
Built in gutters the unseen roof drainage system was specifically chosen to be installed when the home was built thus is part of the original historic character.
Integral gutter eaves trough gutter built in gutter.
Yankee gutters are a drainage system inconspicuously built into the roof so that it isn t visible along the roofline of the house.
They can be a very effective way of managing the flow of water especially on large roofs or complicated water drainage concerns.
They are not readily visible from the ground further lending to the mystery of their design and function.
Instead of hacking off a structurally sound or easily made sound eaves trough or integral gutter that is built into the roof surface you can just roof over it.
I always try to encourage preserving original elements even though it might be easier to eliminate the old method for something new and inexpensive.
These systems are integrated into the design of the roofing structure.
Dating back to the 18th century yankee gutters consist of a v or u shaped wooden trough lined with metal usually copper or terne coated steel that directs water away from the house.
The gutter is built into the roof structure itself as a trough see illustration below.
Sometimes called yankee gutters box gutters or even philadelphia gutters it s no wonder they remain a mystery to many.