Find the area bounded by the curve x^3-3x^2+2x and the x-axis between x=0 and x=1.

To find the area under a curve that is bounded by the x-axis you simply need to integrate the equation of the curve between the limits, so for this equation we will integrate y=x³-3x²+2x with 1 as our upper limit and 0 as our lower limit. To integrate an expression you add 1 to the power and divide by the new power, so the integral of x³-3x²+2x is (1/4)x⁴-x³+x². We then substitute x=1 and x=0 into the expression and subtract the resulting values from eachother. When x=1, (1/4)x⁴-3x³+x²=1/4 and when x=0, (1/4)x⁴-3x³+x²=0. (1/4)-0=1/4 and so that is our final answer to the question.