Given Functions Of $f$ And $g$ , Use the Facts That $\int _ { 0 } ^ { 4 } f ( x ) d x = 4$

Essay

Given functions of $f$ and $g$ , use the facts that $\int _ { 0 } ^ { 4 } f ( x ) d x = 4$ , $\int _ { 4 } ^ { 6 } f ( x ) d x = 3$ $\int _ { 0 } ^ { 6 } g ( x ) d x = - 5 \text {, and } \int _ { 2 } ^ { 6 } g ( x ) d x = - 4$ to evaluate the following integrals:
(a) $\int _ { 0 } ^ { 4 } ( 3 \cdot f ( x ) + 1 ) d x$ (b) $\int _ { 0 } ^ { 6 } f ( x ) d x$ (c) $\int _ { 0 } ^ { 6 } [ f ( x ) - 4 \cdot g ( x ) ] d x$ (d) $\int _ { 0 } ^ { 2 } g ( x ) d x$