area under curve

If $f(x)=2\ln(\sqrt{e^x})$ , what is the area bounded by f(x) for the interval [0, 2] on the x-axis?

Define [x] as the greatest integer less than or equal to x, for each x ϵ (-∞, ∞). If y = [x], then area under y for x ϵ [1,4] is

Area bounded by the curve $$y = {x^2}$$ and the lines $$x=4$$ and $$y=0$$ is given by