be sure to sketch the region whose net area is represented by $B.$

$2.(7$ marks$)$ Evaluate each of the following definite integrals. Remember to show your work, and if you use a substitution or another technique from class make sure you clearly state what you are applying and anything else necessary $($i$.$e$.,$ what function you are substituting$).$

a$.{\displaystyle \underset{1}{\overset{3}{}}}3x^2+4x+1dx$

b$.{\displaystyle \underset{\frac{}{3}}{\overset{}{}}}{e}^{4sin(x)}cos(x)dx$

c$.{\displaystyle \underset{-3}{\overset{-2}{}}}\frac{1}{x^2+6x+10}dx$