Functions to return displacement and velocity from acceleration

I need three functions: 1. displacement_function Inputs: * Starting Displacement in the Y axis. * Starting Velocity in the Y axis. * An array of Time values (X axis). * An array of Acceleration values in the Y axis that correspond to the Time values. Returns: * An array of Displacement values in the Y axis that corresponds to the Time values. 2. velocity_function Inputs: * Starting Displacement in the Y axis.(If needed) * Starting Velocity in the Y axis. * An array of Time values (X axis). * An array of Acceleration values in the Y axis that correspond to the Time values. Returns: * An array of velocity values in the Y axis that corresponds to the Time values. 3. acceleration_derivative_function Inputs: * An array of Time values (X axis). * An array of Acceleration values in the Y axis that correspond to the Time values. Returns: * An array of change in acceleration values in the Y axis that corresponds to the Time values.