[tex] \int\limits^1_0 {f(x)} \, dx = \int\limits^1_0 {(e^x-x)} \, dx = \int\limits^1_0 {e^x} \, dx - \int\limits^1_0 {x} \, dx =\\
=e^x|_0^1- \frac{x^2}{2}|_0^1 =\\
=(e^1-e^0)-( \frac{1^2}{2} - \frac{0^2}{2})=\\
=(e-1)- \frac{1}{2} =\\
=e- \frac{3}{2} [/tex]
