Answer
$\frac{e^2-1}{2e}$
Work Step by Step
$\int^1_0 cosh (t) dt$
The first step is to integrate cosh(t). (Remember that $\int^b_a cosh(x)dx = sinh(x)|^b_a$ and $sinh(x) = \frac{e^x - e^{-x}}{2}$):
$= [sinh(t)]|^1_0$
$= (\frac{e^t - e^{-t}}{2})|^1_0$
Next step is to plug in the limits of integration and simplify until final answer is reached:
$= (\frac{e^1-e^{-1}}{2}) - (\frac{e^0 - e^0}{2})$
$= \frac{e - \frac{1}{e}}{2} - 0$
$= \frac{\frac{e^2 - 1}{e}}{2}$
$= \frac{e^2 - 1}{2e}$