Question

arc length of y= -0.1480x^3+1.353x^2-4.068x+5.651 from x=0.2 to x=5.25

Answer 1

$y=-0.1480x^3+1.353x^2-4.068x+5.651$
$\implies y'=-0.444x^2+2.706x-4.068$

The arc length is given by the integral

$\displaystyle\int_{0.2}^{5.25}\sqrt{1+(y')^2}\,\mathrm dx$

which has a value of about $7.6683$.