The common limit of two series  sn and Sn    is called DEFINITE INTEGRAL of  y(x) continuous function in (x1-x2) interval and is designated by writing:
x2
ò y(x)dx that you must read  "definite integral of y(x)dx from x1 to x2".
x1
The definite integral is a well fixed number when a y(x) function and a (x1-x2) interval are fixed. It is independent of  integration variable values that we then can even replace by any different one. For example t variable. So, if   t1=x1 e t2=x2:
x2	t2
ò y(x)dx =	ò y(t)dt
x1	t1