A particle moves along $x$-axis such that each position is given by $x(t)=2t^3-15t^2+36t+5$, $x$ is expressed in metres. Find the total distance within the time interval $t=0$ second to $t=4$ seconds.
My method: I integrated the equation $x(t)=2t^3-15t^2+36t+5$ to get $116$ metres as the answer. However, according to my sir, the answer is $34$ m. According to him the answer which I got is the displacement of the body and not distance since it depicts the area under the curve formed when a velocity-time graph is drawn.
Now my question is, if $116$ metres is the displacement and $34$ metres is the distance, how is this even possible because displacement can never be more than the distance covered by the body. Please help me. Please clear the doubt and correct my method if wrong.