5. Agreement between definition and shortcut. (TA Supported Calculation) Suppose we define an integral using the limit of a particular Riemann sum: (The details below imply the use of the 'right-point rule' using a uniform partition for all rectangles.) n b - a f(x )dx = lim with Ax= a n-too [ f(at iAx)Ax, n i=1 (a) Take the limit of the Riemann sum construction above to show the value of this limit converges to the same value as the power rule for integration when a = 0, b = 2 and f(x) = x. When you work through the argument you can use the following identities with- out additional proof: n n n(n + 1) = n, i = 2 i=1 i=1(b) Select a new afne function of the form pm +q. (i.e. you pick specific, nonzero numbers for p and q. You can alternately leave them as variables and assume they act like constants) Take the limit of the Riemann sum construction above to Show the value of this limit converges to the same value as the power rule for in tegration when a = 0, b = 2 and you replace f with the afne function you chose