Stuck with integration problem...

Suppose the velocity of an oscillating particle is given by the function .. v(t) = dx/dt = Awsin(wt) where A and w are positive constants.
Find a formula for the displacement x(t) if x(0)=2, A=2 and w=pi

.... I don't even understand what the question is asking me, let alone how to solve it.
Can someone pleaaaasese explain and solve?

So dx/dt is given to be some function. They are asking you to find the anti derivative

So x(t) describes where in time this particle is on the x axis. The change in distance per unit time is the definition of velocity. The change in velocity per unit time is acceleration

So dx/dt= 2pi*sin(pi*t)
Taking the anti derivative of sin(wt) (which is -cos(wt)/w) we get
X(t)= -2pi*cos(pi*t)/pi+c= -2cos(p*t)+c

The c is a constant that disappears when you take the derivative. To determine what c is, we use the information x(0)=2

X(0)=-2cos(pi*0)+c=-2+c=2
C=4
So x(t)=4-2cos(pi*t)

Integrate v(t) to get x(t) = -Acos(wt) + C for some constant C.
Substitute x(0)=2, A=2 and w=pi to solve for C.
2 = -2cos(pi * 0) + C.
Solving for C, you get 4.
Thus, x(t) = -Acos(wt) + 4.

dx/dt = A * w * sin(w * t)
dx = A * w * sin(w * t) * dt
x = -Aw * (1/w) * cos(w * t) + C
x = -A * cos(w * t) + C

x = 2 when t = 0
A = 2
w = pi

2 = -2 * cos(pi * 0) + C
2 = -2 * cos(0) + C
2 = -2 * 1 + C
2 = -2 + C
4 = C

x = -2 * cos(pi * t) + 4