Definite integral to indefine one

[chessmath]

Hi
I would like to know what is the procedure to convert indefinite integral to definite one?
For example I know ∫exp(-u^2)du from 0 to x is equal to ∫x*exp(-x^2*t^2)dt from 0 to 1
But I would like to know with what type of change of variable I get these?

 

[lurflurf]

clearly
u=x t