Find the shaded area in Quadrant 1 between $y=-3 x+10$ and $y=x^{2}$

Step 1 ：First, we need to find the points of intersection of the two curves. This can be done by setting the two equations equal to each other and solving for x.

Step 2 ：Let's set the two equations equal to each other: \(y=-3x+10\) and \(y=x^{2}\).

Step 3 ：Solving for x, we find that the solutions are x = -5 and x = 2.

Step 4 ：However, since we are only interested in Quadrant 1, we discard the negative solution and consider the interval from x = 0 to x = 2.

Step 5 ：The shaded area between two curves can be found by integrating the absolute difference of the two functions over the interval where they intersect.

Step 6 ：Thus, we will integrate the absolute difference of the two functions over the interval from x = 0 to x = 2.

Step 7 ：Performing the integration, we find that the shaded area is \(\frac{343}{6}\) square units.

Step 8 ：Final Answer: The shaded area in Quadrant 1 between \(y=-3x+10\) and \(y=x^{2}\) is \(\boxed{\frac{343}{6}}\) square units.