Working on Front End, Back End and Integration user stories
We have 3 User Stories.
1st-Back End
2nd-Front End
3rd-Integration of Front End with Back End
How should the dev team commit to these user stories as it shows the Horizontal slicing of the work.
What should be the approach to deal with such situations?
Horizontal slicing indicates that the team is no cross-functional.
Scrum recommends vertical slicing, so that value is created per PBI.
We have 3 User Stories.
1st-Back End
2nd-Front End
3rd-Integration of Front End with Back End
Are you sure that from the perspective of the user, they would experience separate features in each case?
How should the dev team commit to these user stories as it shows the Horizontal slicing of the work.
They include all 3 stories in the same sprint and commit by crafting a Sprint Goal that will include the completion of all 3 of these stories.
That helps solve your immediate problem. Now it's time to work on the longer term problem of why the team feels it is necessary to split work horizontally. As @Ian Mitchell indicates, it would be difficult to say that stakeholders would see value if the stories were delivered individually. Each increment a Scrum Team produces should provide value to the stakeholders/users. Each increment builds upon the previous to provide more value.
I don't feel that there is a huge problem slicing in the way that your team has IF those slices are then worked together in a single Sprint. The problem occurs if those slices are not addressed as a single group. Let me use food as an example. You can create a pie crust on its own. You can create a very delicious pie filling on its own. You can make some of the best whipped cream the world has ever known on its own. But the real value is when you put them all together to make a fabulous pie. Don't make people wait for that pie. Do the work in parallel so that the pie can be enjoyed while all of the parts are still fresh.
How should the dev team commit to these user stories as it shows the Horizontal slicing of the work.
The team should not commit to the user story's but to the sprint goal behind these user stories and then select te stories that are needed to meet the sprint goal. in your case the 3 story's you described.
Can the DoD be met for each of these 3 items independently ?