1Indefinite IntegralsThe fundamental theorem of calculus shows just how important antiderivatives are.Since we’ll be usingthem so frequently from now on, we introduce a notation for them. Actually, the FTC gives us an intuitivenotation for them.Definition 1.f(x)dxis an antiderivative off(x). This is called the indefinite integral.*Do a few examplesIt is incredibly important to remember the difference between a definite and an indefinite integral.baf(x)dxis a number andxshouldn’t appear anywhere.f(x)dxis a family of functions and shouldbe nothing butx’s.Here’s a quick reminder of antidifferentiation formulas.*Put up a tableExample 1.1.(18x5-3 secxtanx)dxExample 1.2.sinθcos2θdx*Do a few examples of definite integrals.Finally, recall how I was talking about how the definite integral is a net area or a displacement. Well,another way to state the fundamental theorem of calculus is that the integral of the rate of change is the netchange. *Talk about displacement and then some other examples.Example 1.3.v(t) =t2-t-6. Find the displacement and the distance travelled.