It is currently to my understanding that the area under a $v(t)$ graph is the displacement of an object because $$\int v(t)dt = s(t).$$
However, some of the problems I have attempted recently give you a $v(t)$ formula and ask you to find the total distance travelled. The solution to these problems would be the same solution to finding the position(displacement) of the object.
Are the methods of finding each value the same? If not, what is the difference between each process?