First, Cajori's The History of Notations of the Calculus presents a rather unproblematic history of various notions suggested for the definite integral and none has the limits of integration written on the left.
Second, I checked the textbooks published by The [Indian] National Council of Educational Research and Training (NCERT). They publish textbooks in English, Hindi, and Urdu. The English and the Hindi versions of Year 12 textbook where we can find definite integrals write them as we do. I couldn't find the Urdu version.
Third, and this is the most interesting of all, I checked a number of Youtube videos of some of "famous" (according to the number of viewers) Indian mathematics teachers. They mostly write the lower limit inside on the RIGHT of the integral sign and the upper integral outside on the LEFT of the integral sign. Here are two snapshots of two different teachers.