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

In order to find the area bounded by a curve and the horizontal axis, we must integrate the curve between the specified limits.

Firstly we must integrate the curve x^2-2x+3. To integrate a polynomial such as the one provided above, we must raise the power of each term and divide the term by the new power. Doing this will leave us with (x^3)/3 - x^2 + 3x + C. The new C term there as when integrating it is possible that a new constant can be found.

Now we must apply the limits to the newly integrated equation. This can be done by first substituing the values x=1 into the integrated equation and then minusing the integrated equation with substituted values of x=0: [(1^3)/3 - 1^2 + 3x(1) + C] - [(0^3)/3 - 0^2 + 3(0) + C] = [(1/3) - 1 + 3 + C] - [C] = 7/3.

It should be noted the C values are constant therefore cancel out.

We have now found that the area bounded by the horizontal axis, x=0, x=1 and the curve x^2-2x+3 is 7/3 units of area.