Question

Let f(x) be the function defined by f(x) = {x, x≤0
x+1, x>0

The value of the integral of x(f(x))dx from -2 to 1 =?

Answer 1

f(x) is piecewise. So you must integrate piecewise. The breakpoint is at 0, and the region of integration is [-2,1]. So add the integral over [-2,0] to the integral over [0, 1].