From the trapezium rule
A = d/2{y0 + 2(y1 +y2 + y3+...............+yn-1) + yn}
given int x^cosx dx [0.1,0.7]
take 6 strips............. d = 0.1
calculating the values of y for x = 0.1,0.2.........,0.7
int x^cosx = 0.1/2{0.1 + 2(0.2+0.3+0.4+0.50001+0.60002) + 0.70002}
=0.240004
therefore
Int x^cosx[0.1,0.7] dx = 0.240004