I got these equations (8.3 and 8.4) from the book Introduction to Stochastic processes with R by Dobrow. I cannot for the life of me understand how eq. 8.3 turns into 8.4 by popping out the t variable and changing the lower integration limit to $a/ \sqrt{t}$. As t is both in the denominator as $\sqrt{t}$ and in the exponential as $1/t$..
I tried to find an explanation online but to no avail, anyone that can shed light on this mysterious change of integration limits?