Exercise 2

\[ \int_0^T t^4 \, \mathrm{d}t = \left[ \frac{1}{5} t^5 \right]_0^T = \frac{1}{5} T^5 \] \[ \int_0^T \cos t \, \mathrm{d}t = \left[ \sin t \right]_0^T = \sin T \] \[ \int_0^T t^2 -2 \, \mathrm{d}t = \left[ \frac{1}{3} t^3 - 2t \right]_0^T = \frac{1}{3} T^3-2 T \]