L'Hopital's Rule 0/0 with an integral in the numerator

Find the limit as x approaches 0 of the integral of (1+sint)^(1/2)dt from 0 to x, divided by x. (x is in the denominator)

This is 0/0 format, since the integral in the numerator approaches 0 and the denominator approaches 0, but I don't understand how to get the answer. The integral is with respect to t, and I'm trying to take the derivative with respect to x. It doesn't make sense to me. Can anyone help? The answer in the back of the book says it's 1.