Now imagine dividing the income stream into N pieces instead of 10. (For instance, if you were calculating things one month at a time, N would be 120.) Using notation, write down expressions for an upper bound on the present value of the annuity, a lower bound, and the average. Now take the limit as N +0. Write down a definite integral that gives the present value of the annuity. You are not expected to evaluate this integral. Now imagine dividing the income stream into N pieces instead of 10. (For instance, if you were calculating things one month at a time, N would be 120.) Using notation, write down expressions for an upper bound on the present value of the annuity, a lower bound, and the average. Now take the limit as N +0. Write down a definite integral that gives the present value of the annuity. You are not expected to evaluate this integral