You need to find the exact distance, so a Riemann sum isn't exactly needed but can be used.
The sum-free way to do this is to integrate [tex]f(t)[/tex] over [tex]0\le t\le10[/tex], assuming a starting position of [tex]p_0[/tex].
[tex]p_0+\displaystyle\int_0^{10}f(t)\,\mathrm dt[/tex]
[tex]\implies p_0+\displaystyle3\int_0^{10}t\,\mathrm dt[/tex]
[tex]\implies p_0+\dfrac{3t^2}2\bigg|0^{10}[/tex]
[tex]\implies p_0+150[/tex]
The question says to use a graph (which isn't given), but the idea would have been to find the area under the curve [tex]f(t)=3t[/tex], which would be a triangle whose area would be easy to find.
