By Rajesh Kumar Singh CHICAGO, April 13 (Reuters) - Delta Air Lines DAL.N on Thursday forecast higher-than-expected profit for the second quarter, citing "record" bookings for summer travel, including strong demand for international trips. Travel demand in the United States is currently strong but rising interest rates, persistently high inflation, mounting job losses and a turmoil in the banking industry have cast a shadow over consumer spending. American AirlinesAAL.O on Wednesday forecast first-quarter profit below market expectations, joining rival United Airlines UAL.O in signaling a hit from high labor and fuel costs.