*A charged particle moves along the x-axis under the influence of an electric field. The field strength varies with time, and as a result, the velocity of the particle is complicated. The position of the particle at time t is written as x=x(t) and the velocity of the particle at time t is written as v(t).* *Suppose we know that x(0)=0, and also that* *v(t)={2t-1, if 0*__<__t__<__1 *{4t-3, if 1*__<__t__<__2 *{6t-7, if 2*__<__t__<__3 *What is x(1)? (...find x(2), x(3) and sketch x=x(t), v=v(t))*
So, obviously we can take the antiderivative of v(t) to find x(t) from which you get:

..whats confusing me is the three different intervals for time t. how do i solve for x(1) if there are 2 different antiderivatives for it?? Im confused