Yes, you can file RTI to Integral University. Integral University is a state private university in Lucknow, the capital of Uttar Pradesh, India, which originated as the Institute of Integral Technology, Lucknow. Integral University, the first enacted Minority University in the country, started functioning from 1 April 2004. Integral University was accorded recognition by U.G.C. under section 2(f) of U.G.C. Act, 1956. The University was founded in 2004.
It is a state private university, which doesn't come under the ambit of RTI Act'2005, but we have filed many RTI Applications to private Universities, where we have received RTI responses from few. Having said that, the response rate is low.
For further assistance and to have a better understanding on filing RTI, you may visit the below mentioned link:
https://onlinerti.com/how-to-file-rti-online-for-marksheet