When it comes to systems integration how do you model integration requirements? Do you use UML or BPMN or some other techniques?
What limitiations you see in existing approaches and what would be an ideal modeling approach to system integration requirements in your opinion?
This question is really broad and could be refined (e.g. what level of system?) if you desire a better answer. The approaches below have worked in my experience and were adopted broadly within a company. This may not work for your organization, but our is very application/data integration oriented and these methods help us track integration at high/flow/data entity levels. The key to success is not the ideal model, but a practical one with good training and examples/cheat sheets.
One UML model view that seems to work will for system integration at the component/interface level is a component diagram with components and then interface realizations and interface usages drawn out.
Also using the concept of information flow either UML or just lines with a definition. Then just pick your level of abstraction. Example: PeopleSoft --- (Person Details via File) -----> Active Directory --- (Groups via LDAP) ----> Training Tool.
BPMN is for business process really and though I really think it is great this is not where it should be used.
OMG has tried to answer to your question with the requirement diagram integrated in the sysml modeling langage. SysML tools providers try to solve your problem. For instance check out rational rhapsody solution.