If $f(x)=3.5x^2-2.1x+4.6$ then its arc length from $x=2$ to $x=5$ is given by $$\int_2^5 \sqrt{49x^2-29.4 x+5.41} \,dx$$
The general formula is: $$\int_a^b \sqrt{1+(\frac{dy}{dx})^2} \,dx$$
How do I calculate the first integral without a calculator or a software? Trigonometric substitutions won't work, will they?