Howtosignalprocessing
How do you change bounds of integration?
You want to shift the interval of integration down by 1, so use the change of variables t=x−1. So when x=0, t=−1, and when x=2, t=1. Thus when integrating with respect to t, you would integrate over the interval (−1,1). Be careful to rewrite your integrand in terms of t before solving.
How do you find the upper and lower bounds of an integral?
To find a sum that is an upper bound for an integral, represent the integral as an area and find a sum whose area representation covers that of the integral. This is just the same as finding in upper Riemann sum. Similarly you can find a sum to give a lower bound for an integral, namely a lower Riemann sum.
