$(a)$ Write the following definite integral $as$ a $limit$:

${\displaystyle \underset{7}{\overset{12}{}}}3sin(4x)dx$

$(b)$ Write the following $limitas$ a definite integral:

$\underset{n}{lim}\frac{4}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}[(3+\frac{2i}{n}{)}^2-3(3+\frac{2i}{n})+4]$