$${\theta = \int \omega\, dt = \int (\frac{5}{4} t^4 - 2t^2 + 5) dt \\ = \frac{1}{4}t^5 - \frac{2}{3}t^3 + 5t + C' \\ = \underline{\underline{\frac{1}{4}t^5 - \frac{2}{3}t^3 + 5t + 2}}}$$