don't understand the value of a sum in a curve that has arc length

Hi there

I've got a curve in I know that f(x) is always bigger than zero and the parameter x is between 0 and 1.

Now has arc length which means

. Well somenone today told me that then

must be true. Can someone please explain me why this is true or isn't it true? Yet I don't understand why this has to be equal to 1...

Regards

Re: don't understand the value of a sum in a curve that has arc length

a curve is said to be parameterized by arc length if its tangent vector is of unit length.