Integration

The rate of change of a company's profit (in thousands of dollars per month) is modeled by $P'(t) = (t^2 - 2t + 3)(t^2 + 4t - 1)$. Find the profit function $P(t)$.

The velocity of a particle is given by $v(t) = (t^2 - 3t + 5)^2$ m/s. Determine the displacement function $s(t)$ (ignore the constant of integration).

A particle moves along a line with acceleration $a(t) = 6t - 4$ m/s². If its velocity at time $t=1$ s is $5$ m/s, find the velocity function $v(t)$.