Given the arc lenght, Find the upper/lower limits?

Hi

am thinking about the idea if i know the arc length of spific function

then am asked to know the upper and lower limit

if the lower limit is given and am asked to find the upper limit

it will be easy, as an exaple suppose the arc lenght of f = 5

on [1,Z] find the number z ?

it will be easy I will integrated it as an definite integral then it will be something in terms of z = 5

and solve it

But am asking if the lower and upper limit are unknows, it is possible to find them ? WITHOUT any another given in the problem ?

maybe if the interval is [-Z,Z] and if the function is odd/even

it will be easy a little bit

but if the inteval is [a,b] , not from -a to a

Any help??