How to calculate the exact values of c and d Draw the function $f(x)= x^3-4x^2-13x+10$ into a cartesian plane. If the exact length of that curve from point $P(5,-30)$ to point $Q(c,d)$ is $18$ (with $c>5$), I have no idea how to calculate the values of $c$ and $d$ using the formula $(dx)^2+(dy)^2$. How to approximate the exact values of $c$ and $d$ ? What is the values of $c$ and $d$ (exactly) ?

The formula for arc length from $(a, f(a))$ to $(b, f(b))$ is $L = \int_a^b  \sqrt{1 + (\frac{d (f(x))}{dx})^2}dx$
So the arc length  from $(5,-30)$ to $(c, d=f(c))$ is $L = 18 = \int_5^c \sqrt{1 + \frac{d(x^3-4x^2-13x+10)}{dx}^2}dx$ 
Solve for $c$ and $d = f(c)$.
