Evaluating an integral in physics question $$U_{C} = \frac{1}{C} \int\!\frac{\cos(100\pi t + \pi/4)}{10}\,dt$$
Find $U_{C}$,  the answer is $U_{C}=\left(3.2\times 10^{-4}\right)/C\times \cos(100\pi t - \pi/4)$.
Can someone show to to get this answer?

First, we make the substitution $u = 100\pi t + \pi/4$, so that $du = 100\pi dt$.
Then, substituting, the integral becomes: 
$$U_{c} = \frac{1}{C} \int \cos(u) \cdot \frac{1}{10} \cdot \frac{1}{100\pi}du$$
Integrating, we see that this is:
$$U_{c} = \frac{\frac{1}{1000\pi}}{C}\sin(u) + K$$
or, approximately, with substitution in for $u$:
$$U_{c} = \frac{3.2 \cdot 10^{-4}}{C} \sin(100\pi t + \pi/4) + K$$
Using the fact that $\sin(\theta) = \cos(\theta - \pi/2)$, we see that this is:
$$U_{c} = \frac{3.2 \cdot 10^{-4}}{C} \cos(100\pi t + \pi/4 - \pi/2) + K = \frac{3.2 \cdot 10^{-4}}{C} \cos(100\pi t - \pi/4) + K$$
