Complex line integral $\int_{0}^{\pi+i} |\cos^2(t)| dt$

Question

I want to calculate $\int_{[0,\pi+i]}|\cos^2(t)|dt$.

Now I got $$\int_{[0,\pi+i]}|\cos^2(t)|dt = \int_{0}^{\pi+i}\cos^2(t)dt = \frac{1}{2}(t+\sin(t)\cos(t))|_{t=0}^{t=\pi+i}=\frac{1}{2}(\pi+i+i\sinh(1)\cosh(1))$$ But this way seems too easy, did I do something wrong? Any help is greatly appreciated!