If \([x]\) is the greatest integer function not greater than \(x\), then \(\int_{0}^{11}[x] d x\) is equal to

\(\int_{0}^{11}[x] d x=\int_{0}^{1}[x] d x+\int_{1}^{2}[x] d x\)
\(\quad+\int_{2}^{3}[x] d x+\int_{3}^{4}[x] d x+\int_{4}^{5}[x] d x\)
\(\quad+\int_{5}^{6}[x] d x+\int_{6}^{7}[x] d x+\int_{7}^{8}[x] d x\)
\(\quad+\int_{8}^{9}[x] d x++\int_{9}^{10}[x] d x++\int_{10}^{11}[x] d x\)
\(=\int_{0} 0 d x+\int_{1}^{2} 1 d x+\int_{2}^{3} 2 d x+\int_{3}^{4} 3 d x\)
\(\quad+\int_{4}^{5} 4 d x+\int_{5}^{6} 5 d x+\int_{6}^{7} 6 d x+\int_{7}^{8} 7 d x\)
\(\quad+\int_{8}^{9} 8 d x+\int_{9}^{10} 9 d x+\int_{10}^{11} 10 d x\)
\(=(2-1)+2(3-2)+3(4-3)+4(5-4)\)
\(\quad+5(6-5)+6(7-6)+7(8-7)+8(9-8)\)
\(+9(10-9)+10(11-10)\)
\(=1+2+3+4+5+6+7+8+9+10=55\)