This is called the Cauchy formula for iterated integrals (don't mix it up with the Cauchy formula in complex analysis). Ignore the left hand side. Suppose you were asked to answer the right hand side in an exam. What techniques do you know which would help you?
What I had in mind is expanding the (x-t)^2, and then multiplying everything out, and then I would have 3 separate integrals due to being able to separate integrals based on addition.