1. Let f be a function defined by f(x)=5x2+1. We want to find the area of the surface bounded by the curve y=f(x), the x-axis and the lines x=1 and x=3.

a) Algebraically find Riemann Sum Sn, obtained by dividing the surface into n intervals of equal width and by considering the circumscribed rectangles.

b) Evaluate the area of this surface by findinglimnSn

c) Evaluate the area using the fundamental theorem of calculus (exact value).

2. Evaluate the following integrals:

a)14(x+1)(xx1)dx

b)06(1+sinx)3cosxdx

c)214x212x+95dx